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class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">premjesti</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">sakrij</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">Početak</div> </a> </li> <li id="toc-Formalne_gramatike" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Formalne_gramatike"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Formalne gramatike</span> </div> </a> <ul id="toc-Formalne_gramatike-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Hijerarhija" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Hijerarhija"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Hijerarhija</span> </div> </a> <ul id="toc-Hijerarhija-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Izvori" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Izvori"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Izvori</span> </div> </a> <ul id="toc-Izvori-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Vanjske_poveznice" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Vanjske_poveznice"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Vanjske poveznice</span> </div> </a> <ul id="toc-Vanjske_poveznice-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Sadržaj" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Prikaz sadržaja stranice" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Prikaz sadržaja stranice</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Chomskyjeva hijerarhija</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Idi na druge jezične varijante članka. Dostupan je na 36 jezika" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-36" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">36 jezika</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Chomsky-hi%C3%ABrargie" title="Chomsky-hiërargie – afrikaans" lang="af" hreflang="af" data-title="Chomsky-hiërargie" data-language-autonym="Afrikaans" data-language-local-name="afrikaans" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%B7%D8%A8%D9%82%D8%A7%D8%AA_%D8%A7%D9%84%D9%84%D8%BA%D8%A7%D8%AA_%D8%A7%D9%84%D8%B5%D9%88%D8%B1%D9%8A%D8%A9" title="طبقات اللغات الصورية – arapski" lang="ar" hreflang="ar" data-title="طبقات اللغات الصورية" data-language-autonym="العربية" data-language-local-name="arapski" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%99%D0%B5%D1%80%D0%B0%D1%80%D1%85%D0%B8%D1%8F_%D0%BD%D0%B0_%D0%A7%D0%BE%D0%BC%D1%81%D0%BA%D0%B8" title="Йерархия на Чомски – bugarski" lang="bg" hreflang="bg" data-title="Йерархия на Чомски" data-language-autonym="Български" data-language-local-name="bugarski" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%9A%E0%A6%AE%E0%A7%8D%E2%80%8C%E0%A6%B8%E0%A7%8D%E0%A6%95%E0%A6%BF_%E0%A6%B8%E0%A7%8D%E0%A6%A4%E0%A6%B0%E0%A6%95%E0%A7%8D%E0%A6%B0%E0%A6%AE" title="চম্‌স্কি স্তরক্রম – bangla" lang="bn" hreflang="bn" data-title="চম্‌স্কি স্তরক্রম" data-language-autonym="বাংলা" data-language-local-name="bangla" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Chomskyjeva_hijerarhija" title="Chomskyjeva hijerarhija – bosanski" lang="bs" hreflang="bs" data-title="Chomskyjeva hijerarhija" data-language-autonym="Bosanski" data-language-local-name="bosanski" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Jerarquia_de_Chomsky" title="Jerarquia de Chomsky – katalonski" lang="ca" hreflang="ca" data-title="Jerarquia de Chomsky" data-language-autonym="Català" data-language-local-name="katalonski" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Chomsk%C3%A9ho_hierarchie" title="Chomského hierarchie – češki" lang="cs" hreflang="cs" data-title="Chomského hierarchie" data-language-autonym="Čeština" data-language-local-name="češki" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Chomsky-Hierarchie" title="Chomsky-Hierarchie – njemački" lang="de" hreflang="de" data-title="Chomsky-Hierarchie" data-language-autonym="Deutsch" data-language-local-name="njemački" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%99%CE%B5%CF%81%CE%B1%CF%81%CF%87%CE%AF%CE%B1_%CE%A4%CF%83%CF%8C%CE%BC%CF%83%CE%BA%CE%B9" title="Ιεραρχία Τσόμσκι – grčki" lang="el" hreflang="el" data-title="Ιεραρχία Τσόμσκι" data-language-autonym="Ελληνικά" data-language-local-name="grčki" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Chomsky_hierarchy" title="Chomsky hierarchy – engleski" lang="en" hreflang="en" data-title="Chomsky hierarchy" data-language-autonym="English" data-language-local-name="engleski" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Jerarqu%C3%ADa_de_Chomsky" title="Jerarquía de Chomsky – španjolski" lang="es" hreflang="es" data-title="Jerarquía de Chomsky" data-language-autonym="Español" data-language-local-name="španjolski" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D9%88%D8%B1%D8%A7%D8%AB%D8%AA_%DA%86%D8%A7%D9%85%D8%B3%DA%A9%DB%8C" title="وراثت چامسکی – perzijski" lang="fa" hreflang="fa" data-title="وراثت چامسکی" data-language-autonym="فارسی" data-language-local-name="perzijski" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Chomskyn_hierarkia" title="Chomskyn hierarkia – finski" lang="fi" hreflang="fi" data-title="Chomskyn hierarkia" data-language-autonym="Suomi" data-language-local-name="finski" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Hi%C3%A9rarchie_de_Chomsky" title="Hiérarchie de Chomsky – francuski" lang="fr" hreflang="fr" data-title="Hiérarchie de Chomsky" data-language-autonym="Français" data-language-local-name="francuski" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%94%D7%94%D7%99%D7%A8%D7%A8%D7%9B%D7%99%D7%94_%D7%A9%D7%9C_%D7%97%D7%95%D7%9E%D7%A1%D7%A7%D7%99" title="ההיררכיה של חומסקי – hebrejski" lang="he" hreflang="he" data-title="ההיררכיה של חומסקי" data-language-autonym="עברית" data-language-local-name="hebrejski" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Gerarchia_di_Chomsky" title="Gerarchia di Chomsky – talijanski" lang="it" hreflang="it" data-title="Gerarchia di Chomsky" data-language-autonym="Italiano" data-language-local-name="talijanski" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E3%83%81%E3%83%A7%E3%83%A0%E3%82%B9%E3%82%AD%E3%83%BC%E9%9A%8E%E5%B1%A4" title="チョムスキー階層 – japanski" lang="ja" hreflang="ja" data-title="チョムスキー階層" data-language-autonym="日本語" data-language-local-name="japanski" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%A9%E1%83%9D%E1%83%9B%E1%83%A1%E1%83%99%E1%83%98%E1%83%A1_%E1%83%98%E1%83%94%E1%83%A0%E1%83%90%E1%83%A0%E1%83%A5%E1%83%98%E1%83%90" title="ჩომსკის იერარქია – gruzijski" lang="ka" hreflang="ka" data-title="ჩომსკის იერარქია" data-language-autonym="ქართული" data-language-local-name="gruzijski" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%A5%D0%BE%D0%BC%D1%81%D0%BA%D0%B8%D0%B9_%D0%B8%D0%B5%D1%80%D0%B0%D1%80%D1%85%D0%B8%D1%8F%D1%81%D1%8B" title="Хомский иерархиясы – kazaški" lang="kk" hreflang="kk" data-title="Хомский иерархиясы" data-language-autonym="Қазақша" data-language-local-name="kazaški" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%B4%98%EC%8A%A4%ED%82%A4_%EC%9C%84%EA%B3%84" title="촘스키 위계 – korejski" lang="ko" hreflang="ko" data-title="촘스키 위계" data-language-autonym="한국어" data-language-local-name="korejski" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Hierarchia_Chomskiana" title="Hierarchia Chomskiana – latinski" lang="la" hreflang="la" data-title="Hierarchia Chomskiana" data-language-autonym="Latina" data-language-local-name="latinski" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%A5%D0%B8%D0%B5%D1%80%D0%B0%D1%80%D1%85%D0%B8%D1%98%D0%B0_%D0%BD%D0%B0_%D0%A7%D0%BE%D0%BC%D1%81%D0%BA%D0%B8" title="Хиерархија на Чомски – makedonski" lang="mk" hreflang="mk" data-title="Хиерархија на Чомски" data-language-autonym="Македонски" data-language-local-name="makedonski" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Chomskyhi%C3%ABrarchie" title="Chomskyhiërarchie – nizozemski" lang="nl" hreflang="nl" data-title="Chomskyhiërarchie" data-language-autonym="Nederlands" data-language-local-name="nizozemski" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Chomskyhierarkiet" title="Chomskyhierarkiet – norveški nynorsk" lang="nn" hreflang="nn" data-title="Chomskyhierarkiet" data-language-autonym="Norsk nynorsk" data-language-local-name="norveški nynorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Chomskyhierarkiet" title="Chomskyhierarkiet – norveški bokmål" lang="nb" hreflang="nb" data-title="Chomskyhierarkiet" data-language-autonym="Norsk bokmål" data-language-local-name="norveški bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Hierarchia_Chomsky%E2%80%99ego" title="Hierarchia Chomsky’ego – poljski" lang="pl" hreflang="pl" data-title="Hierarchia Chomsky’ego" data-language-autonym="Polski" data-language-local-name="poljski" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Hierarquia_de_Chomsky" title="Hierarquia de Chomsky – portugalski" lang="pt" hreflang="pt" data-title="Hierarquia de Chomsky" data-language-autonym="Português" data-language-local-name="portugalski" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Ierarhia_Chomsky" title="Ierarhia Chomsky – rumunjski" lang="ro" hreflang="ro" data-title="Ierarhia Chomsky" data-language-autonym="Română" data-language-local-name="rumunjski" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%98%D0%B5%D1%80%D0%B0%D1%80%D1%85%D0%B8%D1%8F_%D0%A5%D0%BE%D0%BC%D1%81%D0%BA%D0%BE%D0%B3%D0%BE" title="Иерархия Хомского – ruski" lang="ru" hreflang="ru" data-title="Иерархия Хомского" data-language-autonym="Русский" data-language-local-name="ruski" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Chomskyjeva_hijerarhija" title="Chomskyjeva hijerarhija – srpsko-hrvatski" lang="sh" hreflang="sh" data-title="Chomskyjeva hijerarhija" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="srpsko-hrvatski" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Chomsky_hierarchy" title="Chomsky hierarchy – Simple English" lang="en-simple" hreflang="en-simple" data-title="Chomsky hierarchy" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Chomsk%C3%A9ho_hierarchia" title="Chomského hierarchia – slovački" lang="sk" hreflang="sk" data-title="Chomského hierarchia" data-language-autonym="Slovenčina" data-language-local-name="slovački" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/Hijerarhija_%C4%8Comskog" title="Hijerarhija Čomskog – srpski" lang="sr" hreflang="sr" data-title="Hijerarhija Čomskog" data-language-autonym="Српски / srpski" data-language-local-name="srpski" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Chomsky_hiyerar%C5%9Fisi" title="Chomsky hiyerarşisi – turski" lang="tr" hreflang="tr" data-title="Chomsky hiyerarşisi" data-language-autonym="Türkçe" data-language-local-name="turski" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a 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href="/w/index.php?title=Posebno:DownloadAsPdf&page=Chomskyjeva_hijerarhija&action=show-download-screen"><span>Preuzmi kao PDF</span></a></li><li id="t-print" class="mw-list-item"><a href="/w/index.php?title=Chomskyjeva_hijerarhija&printable=yes" title="Inačica za ispis ove stranice [p]" accesskey="p"><span>Inačica za ispis</span></a></li> </ul> </div> </div> <div id="p-wikibase-otherprojects" class="vector-menu mw-portlet mw-portlet-wikibase-otherprojects" > <div class="vector-menu-heading"> Wikimedijini projekti </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-wikibase" class="wb-otherproject-link wb-otherproject-wikibase-dataitem mw-list-item"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q190913" title="Poveznica na stavku na projektu Wikipodatci [g]" accesskey="g"><span>Stavka na Wikipodatcima</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> </div> </div> </div> <div class="vector-column-end"> <div class="vector-sticky-pinned-container"> <nav class="vector-page-tools-landmark" aria-label="Pomagala"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Izgled"> <div id="vector-appearance-pinned-container" class="vector-pinned-container"> <div id="vector-appearance" class="vector-appearance vector-pinnable-element"> <div class="vector-pinnable-header vector-appearance-pinnable-header vector-pinnable-header-pinned" data-feature-name="appearance-pinned" data-pinnable-element-id="vector-appearance" data-pinned-container-id="vector-appearance-pinned-container" data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">Izgled</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">premjesti</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">sakrij</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">Izvor: Wikipedija</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="hr" dir="ltr"><p>U <a href="/wiki/Ra%C4%8Dunarstvo" title="Računarstvo">računarstvu</a>, posebice u domeni <a href="/wiki/Programski_jezik" title="Programski jezik">programskih jezika</a>, <b>Chomskyjeva hijerarhija</b> (rjeđe se koristi i termin <b>Chomsky–Schützenbergerova hijerarhija</b>) je hijerarhija klasa <a href="/wiki/Formalna_gramatika" title="Formalna gramatika">formalnih gramatika</a> koje generiraju <a href="/wiki/Formalni_jezik" title="Formalni jezik">formalne jezike</a>. </p><p>Hijerarhiju ovih gramatika (također zvanih i <i>gramatike frazne strukture</i>) je opisao <a href="/wiki/Noam_Chomsky" title="Noam Chomsky">Noam Chomsky</a> 1956. (vidi  <a href="#Izvori">[1]</a>). Također je imenovana po Marcel-Paulu Schützenbergeru koji je odigrao krucijalnu ulogu u razvoju teorije <a href="/wiki/Formalni_jezik" title="Formalni jezik">formalnih jezika</a>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Formalne_gramatike">Formalne gramatike</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Chomskyjeva_hijerarhija&veaction=edit&section=1" title="Uredi odlomak: Formalne gramatike" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Chomskyjeva_hijerarhija&action=edit&section=1" title="Uredi kôd odjeljka Formalne gramatike"><span>uredi kôd</span></a><span class="mw-editsection-bracket">]</span></span></div> <div style="margin-left:0.3rem"><i><style data-mw-deduplicate="TemplateStyles:r7016135">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable"><span typeof="mw:File"><a href="/wiki/Datoteka:Vista-xmag.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e5/Vista-xmag.png/18px-Vista-xmag.png" decoding="async" width="18" height="18" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e5/Vista-xmag.png/27px-Vista-xmag.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e5/Vista-xmag.png/36px-Vista-xmag.png 2x" data-file-width="128" data-file-height="128" /></a></span> Podrobniji članak o temi: <a href="/wiki/Formalna_gramatika" title="Formalna gramatika">Formalna gramatika</a></div></i></div> <p>Formalnu gramatiku čine: </p> <ul><li>konačan skup <a href="/wiki/Zavr%C5%A1ni_i_nezavr%C5%A1ni_znakovi" title="Završni i nezavršni znakovi"><i>završnih znakova</i></a>;</li> <li>konačan skup <a href="/wiki/Zavr%C5%A1ni_i_nezavr%C5%A1ni_znakovi" title="Završni i nezavršni znakovi"><i>nezavršnih znakova</i></a>;</li> <li>konačan skup <i>pravila produkcija</i> čije se lijeve i desne strane sastoje od slijeda takvih znakova</li> <li>istaknuti <i>početni nezavršni znak</i>.</li></ul> <p>Formalna gramatika definira (ili <i>generira</i>) <i>formalni jezik</i>, koji je (moguće beskonačan) skup nizova znakova koji se mogu izgraditi primjenom produkcijskih pravila nad slijedom znakova koji inicijalno sadrži samo istaknuti početni nezavršni znak. Pravilo može biti primijenjeno na međuniz znakova jednostavnom zamjenom pojavljivanja znaka na lijevoj strani produkcije znakovima koji se pojavljuju na desnoj strani. Slijed primjene pravila zovemo <i>produkcija</i> (rijetko i <i>derivacija</i>). Takva gramatika definira formalni jezik čije se riječi sastoje od završnih znakova koji se mogu dohvatiti primjenom produkcija na početni nezavršni znak. </p><p>Nezavršni se znakovi obično pišu velikim slovima, završni malim slovima, dok početni nezavršni znak označavamo specijalnim znakom <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4611d85173cd3b508e67077d4a1252c9c05abca2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.499ex; height:2.176ex;" alt="{\displaystyle S}"></span>. Na primjer, gramatika sa završnim znakovima <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \{a,b\}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo fence="false" stretchy="false">{</mo> <mi>a</mi> <mo>,</mo> <mi>b</mi> <mo fence="false" stretchy="false">}</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \{a,b\}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8127b44bf0e5a64fdc9301e188852ab9b97a1fe8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.586ex; height:2.843ex;" alt="{\displaystyle \{a,b\}}"></span>, nezavršnim znakovima <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \{S,A,B\}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo fence="false" stretchy="false">{</mo> <mi>S</mi> <mo>,</mo> <mi>A</mi> <mo>,</mo> <mi>B</mi> <mo fence="false" stretchy="false">}</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \{S,A,B\}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ce8e7d1a88646df2da6c38d2875340be043eda49" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.399ex; height:2.843ex;" alt="{\displaystyle \{S,A,B\}}"></span>, produkcijama </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4611d85173cd3b508e67077d4a1252c9c05abca2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.499ex; height:2.176ex;" alt="{\displaystyle S}"></span> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \rightarrow \,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">→</mo> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rightarrow \,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/30c77b3d020a207c12a2e96794b739223a647089" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.711ex; height:1.843ex;" alt="{\displaystyle \rightarrow \,}"></span> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle ABS}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mi>B</mi> <mi>S</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ABS}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/940a2a582c1cb1f7f2f94ff021c2b00940a9c41b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.006ex; height:2.176ex;" alt="{\displaystyle ABS}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4611d85173cd3b508e67077d4a1252c9c05abca2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.499ex; height:2.176ex;" alt="{\displaystyle S}"></span> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \rightarrow \,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">→</mo> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rightarrow \,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/30c77b3d020a207c12a2e96794b739223a647089" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.711ex; height:1.843ex;" alt="{\displaystyle \rightarrow \,}"></span> ε (pri čemu je ε <a href="/wiki/Prazni_niz" class="mw-redirect" title="Prazni niz">prazni niz</a>)</dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle BA}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>B</mi> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle BA}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5b8efb97e621ab9b49f8498a49704690bdeb2698" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.507ex; height:2.176ex;" alt="{\displaystyle BA}"></span> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \rightarrow \,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">→</mo> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rightarrow \,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/30c77b3d020a207c12a2e96794b739223a647089" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.711ex; height:1.843ex;" alt="{\displaystyle \rightarrow \,}"></span> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle AB}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mi>B</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle AB}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b04153f9681e5b06066357774475c04aaef3a8bd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.507ex; height:2.176ex;" alt="{\displaystyle AB}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle BS}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>B</mi> <mi>S</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle BS}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cc553968e198340045b509e1211fc15852ea622a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.263ex; height:2.176ex;" alt="{\displaystyle BS}"></span> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \rightarrow \,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">→</mo> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rightarrow \,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/30c77b3d020a207c12a2e96794b739223a647089" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.711ex; height:1.843ex;" alt="{\displaystyle \rightarrow \,}"></span> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle b}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>b</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle b}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f11423fbb2e967f986e36804a8ae4271734917c3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.998ex; height:2.176ex;" alt="{\displaystyle b}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Bb}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>B</mi> <mi>b</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Bb}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a9d7657ebab334a47b95f16d6f7a358d258b65c6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.762ex; height:2.176ex;" alt="{\displaystyle Bb}"></span> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \rightarrow \,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">→</mo> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rightarrow \,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/30c77b3d020a207c12a2e96794b739223a647089" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.711ex; height:1.843ex;" alt="{\displaystyle \rightarrow \,}"></span> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle bb}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>b</mi> <mi>b</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle bb}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d267c182f909b474bb7a008871387e83c504bd7a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.995ex; height:2.176ex;" alt="{\displaystyle bb}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Ab}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mi>b</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Ab}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/88a986a35c66099eabd1de3da32110b5712180d9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.741ex; height:2.176ex;" alt="{\displaystyle Ab}"></span> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \rightarrow \,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">→</mo> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rightarrow \,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/30c77b3d020a207c12a2e96794b739223a647089" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.711ex; height:1.843ex;" alt="{\displaystyle \rightarrow \,}"></span> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle ab}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mi>b</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ab}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/49337c5cf256196e2292f7047cb5da68c24ca95d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.227ex; height:2.176ex;" alt="{\displaystyle ab}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Aa}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mi>a</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Aa}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cecefba498c5dcabc884cedb885f1de8f65fcb27" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.973ex; height:2.176ex;" alt="{\displaystyle Aa}"></span> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \rightarrow \,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">→</mo> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rightarrow \,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/30c77b3d020a207c12a2e96794b739223a647089" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.711ex; height:1.843ex;" alt="{\displaystyle \rightarrow \,}"></span> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle aa}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mi>a</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle aa}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3ced9323514301e38b91f48a114ba6e800f88e54" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.46ex; height:1.676ex;" alt="{\displaystyle aa}"></span></dd></dl> <p>i početnim nezavršnim znakom <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4611d85173cd3b508e67077d4a1252c9c05abca2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.499ex; height:2.176ex;" alt="{\displaystyle S}"></span>, definira jezik svih riječi oblika <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a^{n}b^{n}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> <msup> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a^{n}b^{n}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/43b23197890d3c8fae398ea64a0be1800a89b045" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:4.664ex; height:2.343ex;" alt="{\displaystyle a^{n}b^{n}}"></span> (tj. <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\displaystyle n}"></span> kopija znaka <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ffd2487510aa438433a2579450ab2b3d557e5edc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.23ex; height:1.676ex;" alt="{\displaystyle a}"></span> nakon kojih slijedi <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\displaystyle n}"></span> kopija znaka <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle b}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>b</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle b}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f11423fbb2e967f986e36804a8ae4271734917c3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.998ex; height:2.176ex;" alt="{\displaystyle b}"></span>). Slijedi jednostavna gramatika koja definira sličan jezik: Završni znakovi su <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \{p,q\}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo fence="false" stretchy="false">{</mo> <mi>p</mi> <mo>,</mo> <mi>q</mi> <mo fence="false" stretchy="false">}</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \{p,q\}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bbc4bf30345d33ef9dca8944f51ea15fbb73fb3c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.598ex; height:2.843ex;" alt="{\displaystyle \{p,q\}}"></span>, nezavršni znakovi su <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \{S\}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo fence="false" stretchy="false">{</mo> <mi>S</mi> <mo fence="false" stretchy="false">}</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \{S\}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c538e8a627736d22bbe813ea1682488589378774" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:3.824ex; height:2.843ex;" alt="{\displaystyle \{S\}}"></span>, početni nezavršni znak je <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4611d85173cd3b508e67077d4a1252c9c05abca2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.499ex; height:2.176ex;" alt="{\displaystyle S}"></span>, a produkcije: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4611d85173cd3b508e67077d4a1252c9c05abca2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.499ex; height:2.176ex;" alt="{\displaystyle S}"></span> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \rightarrow \,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">→</mo> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rightarrow \,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/30c77b3d020a207c12a2e96794b739223a647089" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.711ex; height:1.843ex;" alt="{\displaystyle \rightarrow \,}"></span> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle pSq}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>p</mi> <mi>S</mi> <mi>q</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle pSq}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8371c04cb34d01b3bffa9ce305f8bb5a0efca69f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; width:3.828ex; height:2.509ex;" alt="{\displaystyle pSq}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4611d85173cd3b508e67077d4a1252c9c05abca2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.499ex; height:2.176ex;" alt="{\displaystyle S}"></span> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \rightarrow \,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">→</mo> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rightarrow \,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/30c77b3d020a207c12a2e96794b739223a647089" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.711ex; height:1.843ex;" alt="{\displaystyle \rightarrow \,}"></span> ε</dd></dl> <div class="mw-heading mw-heading2"><h2 id="Hijerarhija">Hijerarhija</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Chomskyjeva_hijerarhija&veaction=edit&section=2" title="Uredi odlomak: Hijerarhija" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Chomskyjeva_hijerarhija&action=edit&section=2" title="Uredi kôd odjeljka Hijerarhija"><span>uredi kôd</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Chomskyjeva se hijerarhija sastoji od sljedećih razina: </p> <ul><li>Gramatike tipa 0 (<a href="/wiki/Gramatika_neograni%C4%8Denih_produkcija" title="Gramatika neograničenih produkcija">gramatike neograničenih produkcija</a>) uključuju sve formalne gramatike. Generiraju točno sve jezike koje može prepoznati <a href="/wiki/Turingov_stroj" title="Turingov stroj">Turingov stroj</a>. Ovi su jezici još i poznati kao <a href="/wiki/Rekurzivno_prebrojiv_jezik" title="Rekurzivno prebrojiv jezik">rekurzivno prebrojivi jezici</a>. Uočimo razliku između njih i <a href="/wiki/Rekurzivni_jezik" title="Rekurzivni jezik">rekurzivnih jezika</a> koje <i>odlučuje</i> <a href="/wiki/Stroj_koji_uvijek_staje" title="Stroj koji uvijek staje">Turingov stroj koji uvijek staje</a>.</li> <li>Gramatike tipa 1 (<a href="/wiki/Kontekstno_ovisna_gramatika" title="Kontekstno ovisna gramatika">kontekstno ovisne gramatike</a>) generiraju <a href="/wiki/Kontekstno_ovisni_jezik" title="Kontekstno ovisni jezik">kontekstno ovisne jezike</a>. Ove gramatike imaju produkcije oblika <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \alpha A\beta \rightarrow \alpha \gamma \beta }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>α</mi> <mi>A</mi> <mi>β</mi> <mo stretchy="false">→</mo> <mi>α</mi> <mi>γ</mi> <mi>β</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha A\beta \rightarrow \alpha \gamma \beta }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1173552bcbf68bb06baf9b0a2f543dbc845caefd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:12.259ex; height:2.676ex;" alt="{\displaystyle \alpha A\beta \rightarrow \alpha \gamma \beta }"></span> pri čemu je <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7daff47fa58cdfd29dc333def748ff5fa4c923e3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}"></span> nezavršni znak te <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \alpha }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>α</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b79333175c8b3f0840bfb4ec41b8072c83ea88d3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.488ex; height:1.676ex;" alt="{\displaystyle \alpha }"></span>, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \beta }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>β</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \beta }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7ed48a5e36207156fb792fa79d29925d2f7901e8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.332ex; height:2.509ex;" alt="{\displaystyle \beta }"></span> i <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \gamma }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>γ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \gamma }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a223c880b0ce3da8f64ee33c4f0010beee400b1a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.262ex; height:2.176ex;" alt="{\displaystyle \gamma }"></span> nizovi završnih i nezavršnih znakova. Nizovi znakova <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \alpha }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>α</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b79333175c8b3f0840bfb4ec41b8072c83ea88d3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.488ex; height:1.676ex;" alt="{\displaystyle \alpha }"></span> i <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \beta }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>β</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \beta }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7ed48a5e36207156fb792fa79d29925d2f7901e8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.332ex; height:2.509ex;" alt="{\displaystyle \beta }"></span> mogu biti prazni, ali niz znakova <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \gamma }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>γ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \gamma }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a223c880b0ce3da8f64ee33c4f0010beee400b1a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.262ex; height:2.176ex;" alt="{\displaystyle \gamma }"></span> mora biti neprazan. Produkcija <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S\rightarrow \epsilon }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> <mo stretchy="false">→</mo> <mi>ϵ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S\rightarrow \epsilon }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b118a2c5fb5cbe4c11e07687a2b702019d508431" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.057ex; height:2.176ex;" alt="{\displaystyle S\rightarrow \epsilon }"></span> je dozvoljena ako se <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4611d85173cd3b508e67077d4a1252c9c05abca2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.499ex; height:2.176ex;" alt="{\displaystyle S}"></span> ne pojavljuje na desnoj strani neke produkcije. Jezici koje gramatike ovog tipa opisuju su točno svi jezici koje može prepoznati <a href="/wiki/Linearno_ograni%C4%8Den_automat" title="Linearno ograničen automat">linearno ograničen automat</a> (nedeterministički Turingov stroj čija je traka ograničena konstantom puta duljina ulaza.)</li> <li>Gramatike tipa 2 (<a href="/wiki/Kontekstno_neovisna_gramatika" title="Kontekstno neovisna gramatika">kontekstno neovisne gramatike</a>) generiraju <a href="/wiki/Kontekstno_neovisni_jezik" title="Kontekstno neovisni jezik">kontekstno neovisne jezike</a>. Imaju produkcije oblika <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A\rightarrow \gamma }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo stretchy="false">→</mo> <mi>γ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A\rightarrow \gamma }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/91998fd76701871c7df169d4e9114b5970c61877" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.62ex; height:2.676ex;" alt="{\displaystyle A\rightarrow \gamma }"></span> pri čemu je <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7daff47fa58cdfd29dc333def748ff5fa4c923e3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}"></span> nezavršni znak i <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \gamma }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>γ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \gamma }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a223c880b0ce3da8f64ee33c4f0010beee400b1a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.262ex; height:2.176ex;" alt="{\displaystyle \gamma }"></span> niz završnih i nezavršnih znakova. Ovi jezici su točno svi oni jezici koje može prepoznati nedeterministički <a href="/wiki/Potisni_automat" title="Potisni automat">potisni automat</a>. Kontekstno neovisni jezici su teoretska baza za sintaksu većine <a href="/wiki/Programski_jezik" title="Programski jezik">programskih jezika</a>.</li> <li>Gramatika tipa 3 (<a href="/wiki/Regularna_gramatika" title="Regularna gramatika">regularne gramatike</a>) generiraju <a href="/wiki/Regularni_jezik" title="Regularni jezik">regularne jezike</a>. Takva gramatika ograničava svoje produkcije na jedan nezavršni znak na lijevoj strani produkcije pri čemu se desna strana može sastojati samo od jednog završnog znaka, nakon kojeg slijedi (ili prethodi, ali ne i oboje u istoj gramatici) jedan nezavršni znak. Produkcija <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S\rightarrow \epsilon }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> <mo stretchy="false">→</mo> <mi>ϵ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S\rightarrow \epsilon }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b118a2c5fb5cbe4c11e07687a2b702019d508431" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.057ex; height:2.176ex;" alt="{\displaystyle S\rightarrow \epsilon }"></span> je ovdje također dozvoljena ako se <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4611d85173cd3b508e67077d4a1252c9c05abca2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.499ex; height:2.176ex;" alt="{\displaystyle S}"></span> ne pojavljuje na desnoj strani neke od produkcija. Ovi jezici su točno svi oni jezici koje može odlučiti <a href="/wiki/Kona%C4%8Dni_automat" title="Konačni automat">konačni automat</a>. Dodatno, ova familija formalnih jezika može biti opisana <a href="/wiki/Regularni_izraz" title="Regularni izraz">regularnim izrazima</a>. Regularni jezici se obično koriste za definiranje uzoraka pretrage te analizu leksičke strukture programskog jezika.</li></ul> <p>Uočimo da skup gramatika koji odgovara rekurzivnim jezicima nije prisutan u ovoj hijerarhiji. </p><p>Svaki regularni jezik je kontekstno neovisan, svaki kontekstno neovisni jezik je kontekstno ovisan, svaki kontekstno ovisni jezik je rekurzivan i svaki rekurzivni jezik je rekurzivno prebrojiv. Ovo su sve pravi podskupovi (inkluzije), što znači da postoje nerekurzivni rekurzivno prebrojivi jezici, rekurzivni jezici koji nisu kontekstno ovisni, kontekstno ovisni jezici koji nisu kontekstno neovisni kao i neregularni kontekstno neovisni jezici. </p><p>Sljedeća tablica predstavlja sažetak tipova gramatika u Chomskyjevoj hijerarhiji, klase jezika koje generiraju, tip automata koji ih prepoznaje, te oblik produkcija koje moraju imati. </p> <table class="wikitable"> <tbody><tr> <th>Gramatika </th> <th>Jezici </th> <th>Automat </th> <th>Pravila produkcija </th></tr> <tr> <td>Tip 0 </td> <td><a href="/wiki/Rekurzivno_prebrojiv_jezik" title="Rekurzivno prebrojiv jezik">Rekurzivno prebrojivi</a> </td> <td><a href="/wiki/Turingov_stroj" title="Turingov stroj">Turingov stroj</a> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \alpha \rightarrow \beta }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>α</mi> <mo stretchy="false">→</mo> <mi>β</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha \rightarrow \beta }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0e2b0511d452842ec71e40223d223472b7527ca7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.434ex; height:2.509ex;" alt="{\displaystyle \alpha \rightarrow \beta }"></span> (bez ograničenja) </td></tr> <tr> <td>Tip 1 </td> <td><a href="/wiki/Kontekstno_ovisna_gramatika" title="Kontekstno ovisna gramatika">Kontekstno ovisna</a> </td> <td><a href="/wiki/Linearno_ograni%C4%8Den_automat" title="Linearno ograničen automat">Linearno ograničeni nedeterministički Turingov stroj</a> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \alpha A\beta \rightarrow \alpha \gamma \beta }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>α</mi> <mi>A</mi> <mi>β</mi> <mo stretchy="false">→</mo> <mi>α</mi> <mi>γ</mi> <mi>β</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha A\beta \rightarrow \alpha \gamma \beta }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1173552bcbf68bb06baf9b0a2f543dbc845caefd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:12.259ex; height:2.676ex;" alt="{\displaystyle \alpha A\beta \rightarrow \alpha \gamma \beta }"></span> </td></tr> <tr> <td>Tip 2 </td> <td><a href="/wiki/Kontekstno_neovisna_gramatika" title="Kontekstno neovisna gramatika">Kontekstno neovisna</a> </td> <td>Nedeterministički <a href="/wiki/Potisni_automat" title="Potisni automat">potisni automat</a> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A\rightarrow \gamma }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo stretchy="false">→</mo> <mi>γ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A\rightarrow \gamma }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/91998fd76701871c7df169d4e9114b5970c61877" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.62ex; height:2.676ex;" alt="{\displaystyle A\rightarrow \gamma }"></span> </td></tr> <tr> <td>Tip 3 </td> <td><a href="/wiki/Regularna_gramatika" title="Regularna gramatika">Regularna</a> </td> <td><a href="/wiki/Kona%C4%8Dni_automat" title="Konačni automat">Konačni automat</a> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A\rightarrow \epsilon }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo stretchy="false">→</mo> <mi>ϵ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A\rightarrow \epsilon }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/98e83945fcc69fc13eb0b7a71e35590efcb1aa94" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.301ex; height:2.176ex;" alt="{\displaystyle A\rightarrow \epsilon }"></span> i<br /><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A\rightarrow aB}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo stretchy="false">→</mo> <mi>a</mi> <mi>B</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A\rightarrow aB}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/01b2bfd09f27542fbcf3811786b84f6a43fd17d3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:8.351ex; height:2.176ex;" alt="{\displaystyle A\rightarrow aB}"></span> </td></tr></tbody></table> <div class="mw-heading mw-heading2"><h2 id="Izvori">Izvori</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Chomskyjeva_hijerarhija&veaction=edit&section=3" title="Uredi odlomak: Izvori" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Chomskyjeva_hijerarhija&action=edit&section=3" title="Uredi kôd odjeljka Izvori"><span>uredi kôd</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><style data-mw-deduplicate="TemplateStyles:r7012897">.mw-parser-output cite.citation{font-style:inherit}.mw-parser-output .citation q{quotes:"»""«"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .citation .cs1-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/thumb/6/65/Lock-green.svg/9px-Lock-green.svg.png")no-repeat;background-position:right .1em center}.mw-parser-output .citation .cs1-lock-limited a,.mw-parser-output .citation .cs1-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/thumb/d/d6/Lock-gray-alt-2.svg/9px-Lock-gray-alt-2.svg.png")no-repeat;background-position:right .1em center}.mw-parser-output .citation .cs1-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/thumb/a/aa/Lock-red-alt-2.svg/9px-Lock-red-alt-2.svg.png")no-repeat;background-position:right .1em center}.mw-parser-output .cs1-subscription,.mw-parser-output .cs1-registration{color:#555}.mw-parser-output .cs1-subscription span,.mw-parser-output .cs1-registration span{border-bottom:1px dotted;cursor:help}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Wikisource-logo.svg/12px-Wikisource-logo.svg.png")no-repeat;background-position:right .1em center}.mw-parser-output code.cs1-code{color:inherit;background:inherit;border:inherit;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;font-size:100%}.mw-parser-output .cs1-visible-error{font-size:100%}.mw-parser-output .cs1-maint{display:none;color:#33aa33;margin-left:0.3em}.mw-parser-output .cs1-subscription,.mw-parser-output .cs1-registration,.mw-parser-output .cs1-format{font-size:95%}.mw-parser-output .cs1-kern-left,.mw-parser-output .cs1-kern-wl-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right,.mw-parser-output .cs1-kern-wl-right{padding-right:0.2em}</style><cite id="CITEREFChomsky1956" class="citation journal cs1">Chomsky, Noam. 1956. Three models for the description of language. <i>IRE Transactions on Information Theory</i> (2): 113–124</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=IRE+Transactions+on+Information+Theory&rft.atitle=Three+models+for+the+description+of+language&rft.issue=2&rft.pages=113-124&rft.date=1956&rft.aulast=Chomsky&rft.aufirst=Noam&rfr_id=info%3Asid%2Fhr.wikipedia.org%3AChomskyjeva+hijerarhija" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r7012897"><cite id="CITEREFChomsky1959" class="citation journal cs1">Chomsky, Noam. 1959. On certain formal properties of grammars. <i>Information and Control</i> (2): 137–167</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Information+and+Control&rft.atitle=On+certain+formal+properties+of+grammars&rft.issue=2&rft.pages=137-167&rft.date=1959&rft.aulast=Chomsky&rft.aufirst=Noam&rfr_id=info%3Asid%2Fhr.wikipedia.org%3AChomskyjeva+hijerarhija" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r7012897"><cite id="CITEREFChomskySchützenberger1963" class="citation book cs1">Chomsky, Noam; Schützenberger, Marcel P. 1963. The algebraic theory of context free languages. Braffort, P.; Hirschberg, D. (ur.). <i>Computer Programming and Formal Languages</i>. North Holland. Amsterdam. str. 118–161</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=The+algebraic+theory+of+context+free+languages&rft.btitle=Computer+Programming+and+Formal+Languages&rft.place=Amsterdam&rft.pages=118-161&rft.pub=North+Holland&rft.date=1963&rft.aulast=Chomsky&rft.aufirst=Noam&rft.au=Sch%C3%BCtzenberger%2C+Marcel+P.&rfr_id=info%3Asid%2Fhr.wikipedia.org%3AChomskyjeva+hijerarhija" class="Z3988"></span><span class="cs1-maint citation-comment">CS1 održavanje: više imena: editors list (<a href="/wiki/Kategorija:CS1_odr%C5%BEavanje:_vi%C5%A1e_imena:_editors_list" title="Kategorija:CS1 održavanje: više imena: editors list">link</a>)</span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r7012897"><cite id="CITEREFSiniša_Srbljić2003" class="citation book cs1">Siniša Srbljić. 2003. <i>Jezični procesori 1</i>. Element. <a href="/wiki/Me%C4%91unarodni_standardni_knji%C5%BEni_broj" title="Međunarodni standardni knjižni broj">ISBN</a> <a href="/wiki/Posebno:Tra%C5%BEi_ISBN/953-197-129-3" title="Posebno:Traži ISBN/953-197-129-3">953-197-129-3</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Jezi%C4%8Dni+procesori+1&rft.pub=Element&rft.date=2003&rft.au=Sini%C5%A1a+Srblji%C4%87&rfr_id=info%3Asid%2Fhr.wikipedia.org%3AChomskyjeva+hijerarhija" class="Z3988"></span></li></ul> <div class="mw-heading mw-heading2"><h2 id="Vanjske_poveznice">Vanjske poveznice</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Chomskyjeva_hijerarhija&veaction=edit&section=4" title="Uredi odlomak: Vanjske poveznice" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Chomskyjeva_hijerarhija&action=edit&section=4" title="Uredi kôd odjeljka Vanjske poveznice"><span>uredi kôd</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external free" href="http://www.staff.ncl.ac.uk/hermann.moisl/ell236/lecture5.htm">http://www.staff.ncl.ac.uk/hermann.moisl/ell236/lecture5.htm</a></li></ul> <table align="center" border="0" cellpadding="2" cellspacing="0" class="toccolours"> <tbody><tr> <th colspan="4" style="background:#ddd;"><a href="/wiki/Teorija_automata" title="Teorija automata">Teorija automata</a>: <a href="/wiki/Formalni_jezik" title="Formalni jezik">formalni jezici</a> i <a href="/wiki/Formalna_gramatika" title="Formalna gramatika">formalne gramatike</a> </th></tr> <tr align="left"> <th style="border-bottom:2px solid"><b><a class="mw-selflink selflink">Chomskyjeva<br />hijerarhija</a></b> </th> <th style="border-bottom:2px solid"><b><a href="/wiki/Formalna_gramatika" title="Formalna gramatika">Gramatike</a></b> </th> <th style="border-bottom:2px solid"><b><a href="/wiki/Formalni_jezik" title="Formalni jezik">Jezici</a></b> </th> <th style="border-bottom:2px solid"><b>Minimalni<br /><a href="/wiki/Kona%C4%8Dni_automat" title="Konačni automat">automat</a></b> </th></tr> <tr align="left"> <td>Tip 0 </td> <td><a href="/wiki/Gramatika_neograni%C4%8Denih_produkcija" title="Gramatika neograničenih produkcija">Neograničenih produkcija</a> </td> <td><a href="/wiki/Rekurzivno_prebrojiv_jezik" title="Rekurzivno prebrojiv jezik">Rekurzivno prebrojiv</a> </td> <td><a href="/wiki/Turingov_stroj" title="Turingov stroj">Turingov stroj</a> </td></tr> <tr align="left"> <td>n/a </td> <td>(nema uobičajenog imena) </td> <td><a href="/wiki/Rekurzivni_jezik" title="Rekurzivni jezik">Rekurzivni</a> </td> <td><a href="/wiki/Stroj_koji_uvijek_staje" title="Stroj koji uvijek staje">Odlučitelj</a> </td></tr> <tr align="left"> <td>Tip 1 </td> <td><a href="/wiki/Kontekstno_ovisna_gramatika" title="Kontekstno ovisna gramatika">Kontekstno ovisna</a> </td> <td><a href="/wiki/Kontekstno_ovisni_jezik" title="Kontekstno ovisni jezik">Kontekstno ovisni</a> </td> <td><a href="/wiki/Linearno_ograni%C4%8Den_automat" title="Linearno ograničen automat">Linearno ograničen</a> </td></tr> <tr align="left"> <td>n/a </td> <td><a href="/w/index.php?title=Indeksirana_gramatika&action=edit&redlink=1" class="new" title="Indeksirana gramatika (stranica ne postoji)">Indeksirana</a> </td> <td><a href="/wiki/Indeksirani_jezik" title="Indeksirani jezik">Indeksirani</a> </td> <td><a href="/wiki/Automat_sa_ugnije%C5%BE%C4%91enim_stogom" class="mw-redirect" title="Automat sa ugniježđenim stogom">Ugniježđenog stoga</a> </td></tr> <tr align="left"> <td>Tip 2 </td> <td><a href="/wiki/Kontekstno_neovisna_gramatika" title="Kontekstno neovisna gramatika">Kontekstno neovisna</a> </td> <td><a href="/wiki/Kontekstno_neovisni_jezik" title="Kontekstno neovisni jezik">Kontekstno neovisni</a> </td> <td><a href="/wiki/Potisni_automat" title="Potisni automat">Nedeterministički potisni</a> </td></tr> <tr align="left"> <td>n/a </td> <td><a href="/wiki/Deterministi%C4%8Dka_kontekstno_neovisna_gramatika" title="Deterministička kontekstno neovisna gramatika">Deterministička kontekstno neovisna</a> </td> <td><a href="/wiki/Deterministi%C4%8Dki_kontekstno_neovisni_jezik" title="Deterministički kontekstno neovisni jezik">Deterministički kontekstno neovisni</a> </td> <td><a href="/wiki/Deterministi%C4%8Dki_potisni_automat" title="Deterministički potisni automat">Deterministički potisni</a> </td></tr> <tr align="left"> <td>Tip 3 </td> <td><a href="/wiki/Regularna_gramatika" title="Regularna gramatika">Regularna</a> </td> <td><a href="/wiki/Regularni_jezik" title="Regularni jezik">Regularni</a> </td> <td><a href="/wiki/Kona%C4%8Dni_automat" title="Konačni automat">Konačni</a> </td></tr> <tr> <th style="border-top:2px solid" colspan="4"><small>Svaka kategorija jezika ili gramatika je pravi podskup nadređene kategorije.</small> </th></tr> </tbody></table>    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