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Regularni jezik – Wikipedija

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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-Regularni_jezici_nad_abecedom" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Regularni_jezici_nad_abecedom"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Regularni jezici nad abecedom</span> </div> </a> <ul id="toc-Regularni_jezici_nad_abecedom-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Svojstva_zatvorenosti" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Svojstva_zatvorenosti"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Svojstva zatvorenosti</span> </div> </a> <ul id="toc-Svojstva_zatvorenosti-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Odlučivanje_regularnosti_jezika" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Odlučivanje_regularnosti_jezika"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Odlučivanje regularnosti jezika</span> </div> </a> <ul id="toc-Odlučivanje_regularnosti_jezika-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Konačni_jezici" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Konačni_jezici"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Konačni jezici</span> </div> </a> <ul id="toc-Konačni_jezici-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">5</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">6</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">Regularni jezik</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 24 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-24" 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">24 jezika</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Llenguatge_regular" title="Llenguatge regular – katalonski" lang="ca" hreflang="ca" data-title="Llenguatge regular" 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/Regul%C3%A1rn%C3%AD_jazyk" title="Regulární jazyk – češki" lang="cs" hreflang="cs" data-title="Regulární jazyk" 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/Regul%C3%A4re_Sprache" title="Reguläre Sprache – njemački" lang="de" hreflang="de" data-title="Reguläre Sprache" 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%9A%CE%B1%CE%BD%CE%BF%CE%BD%CE%B9%CE%BA%CE%AE_%CE%B3%CE%BB%CF%8E%CF%83%CF%83%CE%B1" title="Κανονική γλώσσα – grčki" lang="el" hreflang="el" data-title="Κανονική γλώσσα" 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/Regular_language" title="Regular language – engleski" lang="en" hreflang="en" data-title="Regular language" 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/Lenguaje_regular" title="Lenguaje regular – španjolski" lang="es" hreflang="es" data-title="Lenguaje regular" 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/%D8%B2%D8%A8%D8%A7%D9%86_%D9%85%D9%86%D8%B8%D9%85" title="زبان منظم – perzijski" lang="fa" hreflang="fa" data-title="زبان منظم" 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/S%C3%A4%C3%A4nn%C3%B6llinen_kieli" title="Säännöllinen kieli – finski" lang="fi" hreflang="fi" data-title="Säännöllinen kieli" 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/Langage_rationnel" title="Langage rationnel – francuski" lang="fr" hreflang="fr" data-title="Langage rationnel" 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%A9%D7%A4%D7%94_%D7%A8%D7%92%D7%95%D7%9C%D7%A8%D7%99%D7%AA" title="שפה רגולרית – hebrejski" lang="he" hreflang="he" data-title="שפה רגולרית" data-language-autonym="עברית" data-language-local-name="hebrejski" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Regul%C3%A1ris_nyelv" title="Reguláris nyelv – mađarski" lang="hu" hreflang="hu" data-title="Reguláris nyelv" data-language-autonym="Magyar" data-language-local-name="mađarski" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Linguaggio_regolare" title="Linguaggio regolare – talijanski" lang="it" hreflang="it" data-title="Linguaggio regolare" 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/%E6%AD%A3%E8%A6%8F%E8%A8%80%E8%AA%9E" title="正規言語 – japanski" lang="ja" hreflang="ja" data-title="正規言語" 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-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%A0%95%EA%B7%9C_%EC%96%B8%EC%96%B4" title="정규 언어 – korejski" lang="ko" hreflang="ko" data-title="정규 언어" data-language-autonym="한국어" data-language-local-name="korejski" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-mwl mw-list-item"><a href="https://mwl.wikipedia.org/wiki/Lenguaiges_regulares" title="Lenguaiges regulares – mirandski" lang="mwl" hreflang="mwl" data-title="Lenguaiges regulares" data-language-autonym="Mirandés" data-language-local-name="mirandski" class="interlanguage-link-target"><span>Mirandés</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Reguliere_taal" title="Reguliere taal – nizozemski" lang="nl" hreflang="nl" data-title="Reguliere taal" data-language-autonym="Nederlands" data-language-local-name="nizozemski" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Regul%C3%A6rt_spr%C3%A5k" title="Regulært språk – norveški bokmål" lang="nb" hreflang="nb" data-title="Regulært språk" 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/J%C4%99zyk_regularny" title="Język regularny – poljski" lang="pl" hreflang="pl" data-title="Język regularny" 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/Linguagem_regular" title="Linguagem regular – portugalski" lang="pt" hreflang="pt" data-title="Linguagem regular" 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/Limbaj_regulat" title="Limbaj regulat – rumunjski" lang="ro" hreflang="ro" data-title="Limbaj regulat" 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%A0%D0%B5%D0%B3%D1%83%D0%BB%D1%8F%D1%80%D0%BD%D1%8B%D0%B9_%D1%8F%D0%B7%D1%8B%D0%BA" title="Регулярный язык – ruski" lang="ru" hreflang="ru" data-title="Регулярный язык" data-language-autonym="Русский" data-language-local-name="ruski" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/Regularni_jezik" title="Regularni jezik – srpski" lang="sr" hreflang="sr" data-title="Regularni jezik" 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-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%A0%D0%B5%D0%B3%D1%83%D0%BB%D1%8F%D1%80%D0%BD%D0%B0_%D0%BC%D0%BE%D0%B2%D0%B0" title="Регулярна мова – ukrajinski" lang="uk" hreflang="uk" data-title="Регулярна мова" data-language-autonym="Українська" data-language-local-name="ukrajinski" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E6%AD%A3%E5%88%99%E8%AF%AD%E8%A8%80" title="正则语言 – kineski" lang="zh" hreflang="zh" data-title="正则语言" data-language-autonym="中文" data-language-local-name="kineski" class="interlanguage-link-target"><span>中文</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q752532#sitelinks-wikipedia" title="Poveznice na druge jezike" class="wbc-editpage">Uredi poveznice</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="Imenski prostori"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-main" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Regularni_jezik" title="Pogledaj sadržaj [c]" accesskey="c"><span>Stranica</span></a></li><li id="ca-talk" class="new vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Razgovor:Regularni_jezik&amp;action=edit&amp;redlink=1" rel="discussion" class="new" title="Razgovorna stranica (stranica ne postoji) [t]" accesskey="t"><span>Razgovor</span></a></li> </ul> </div> </div> <div id="vector-variants-dropdown" class="vector-dropdown emptyPortlet" > <input type="checkbox" id="vector-variants-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-variants-dropdown" class="vector-dropdown-checkbox " aria-label="Promijeni jezičnu varijantu" > <label id="vector-variants-dropdown-label" for="vector-variants-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">hrvatski</span> </label> <div class="vector-dropdown-content"> <div id="p-variants" class="vector-menu mw-portlet mw-portlet-variants emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> </div> </div> </nav> </div> <div id="right-navigation" class="vector-collapsible"> <nav aria-label="Pogledi"> <div id="p-views" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-views" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-view" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Regularni_jezik"><span>Čitaj</span></a></li><li id="ca-ve-edit" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Regularni_jezik&amp;veaction=edit" title="Uredite ovu stranicu [v]" accesskey="v"><span>Uredi</span></a></li><li id="ca-edit" class="collapsible vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Regularni_jezik&amp;action=edit" title="Uredite izvorni kôd ove stranice [e]" accesskey="e"><span>Uredi kôd</span></a></li><li id="ca-history" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Regularni_jezik&amp;action=history" title="Ranije izmjene na ovoj stranici [h]" accesskey="h"><span>Vidi povijest</span></a></li> </ul> </div> </div> </nav> <nav class="vector-page-tools-landmark" aria-label="Pomagala"> <div id="vector-page-tools-dropdown" class="vector-dropdown vector-page-tools-dropdown" > <input type="checkbox" id="vector-page-tools-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-tools-dropdown" class="vector-dropdown-checkbox " aria-label="Pomagala" > <label id="vector-page-tools-dropdown-label" for="vector-page-tools-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">Pomagala</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-tools-unpinned-container" class="vector-unpinned-container"> <div id="vector-page-tools" class="vector-page-tools vector-pinnable-element"> <div 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class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="hr" dir="ltr"><p><b>Regularni jezik</b> (još i <b>pravilni jezik</b><sup id="cite_ref-InfoRjecnik_1-0" class="reference"><a href="#cite_note-InfoRjecnik-1"><span class="cite-bracket">&#91;</span>1<span class="cite-bracket">&#93;</span></a></sup>) jest <a href="/wiki/Formalni_jezik" title="Formalni jezik">formalni jezik</a> (tj. potencijalno beskonačan skup konačnih slijedova znakova konačne <a href="/wiki/Abeceda_(ra%C4%8Dunarstvo)" title="Abeceda (računarstvo)">abecede</a>) koji zadovoljava sljedeća istovjetna svojstva: </p> <ul><li>može ga prihvatiti <a href="/wiki/Deterministi%C4%8Dki_kona%C4%8Dni_automat" title="Deterministički konačni automat">deterministički konačni automat</a></li> <li>može ga prihvatiti <a href="/wiki/Nedeterministi%C4%8Dki_kona%C4%8Dni_automat" title="Nedeterministički konačni automat">nedeterministički konačni automat</a></li> <li>može ga prihvatiti <a href="/wiki/Alterniraju%C4%87i_kona%C4%8Dni_automat" title="Alternirajući konačni automat">alternirajući konačni automat</a></li> <li>može biti opisan <a href="/wiki/Regularni_izraz" title="Regularni izraz">regularnim izrazom</a></li> <li>može ga generirati <a href="/wiki/Regularna_gramatika" title="Regularna gramatika">regularna gramatika</a></li> <li>može ga generirati <a href="/wiki/Prefiksna_gramatika" title="Prefiksna gramatika">prefiksna gramatika</a></li> <li>može ga prihvatiti <a href="/wiki/Turingov_stroj" title="Turingov stroj">Turingov stroj</a> čija glava samo čita znakove ulazne trake</li> <li>može se definirati u monadičkoj logici drugog reda</li></ul> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Regularni_jezici_nad_abecedom">Regularni jezici nad abecedom</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Regularni_jezik&amp;veaction=edit&amp;section=1" title="Uredi odlomak: Regularni jezici nad abecedom" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Regularni_jezik&amp;action=edit&amp;section=1" title="Uredi kôd odjeljka Regularni jezici nad abecedom"><span>uredi kôd</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Skup svih regularnih jezika nad abecedom &#931; je definiran rekurzivno na sljedeći način: </p> <ul><li>Prazni jezik Ø je regularni jezik.</li> <li>Jezik <a href="/wiki/Prazni_niz" class="mw-redirect" title="Prazni niz">praznog niza</a> { &#949; } je regularni jezik.</li> <li>Za svaki <i>a</i> ∈ &#931;, singleton { <i>a</i> } je regularni jezik.</li> <li>Ako su <i>A</i> i <i>B</i> regularni jezici, tada su <i>A</i> ∪ <i>B</i> (unija), <i>A</i> &#8226; <i>B</i> (nadovezivanje) te <i>A</i>* (<a href="/wiki/Kleeneov_operator" title="Kleeneov operator">Kleeneov operator</a>) također regularni jezici.</li> <li>Nijedan drugi jezik nad &#931; nije regularan.</li></ul> <p>Svi konačni jezici su regularni. Ostali tipični primjeri regularnih jezika uključuju jezik koji se sastoji od svih nizova znakova (stringova) nad abecedom {<i>a</i>, <i>b</i>} koji sadrže paran broj znakova <i>a</i>, ili jezik koji se sastoji od svih nizova znakova oblika: nekoliko znakova <i>a</i> nakon kojih slijedi nekoliko znakova <i>b</i>. </p><p>Ako jezik <i>nije</i> regularan, tada stroj koji ga prepoznaje mora imati najmanje &#937;(log log <i>n</i>) prostora (gdje je <i>n</i> duljina ulaznog niza). Drugim riječima, klasa složenosti DSPACE(o(log log <i>n</i>)) je jednaka klasi regularnih jezika. U praksi je većina neregularnih problema riješiva strojevima koji uzimaju prostor najmanje logaritamske složenosti. </p> <div class="mw-heading mw-heading2"><h2 id="Svojstva_zatvorenosti">Svojstva zatvorenosti</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Regularni_jezik&amp;veaction=edit&amp;section=2" title="Uredi odlomak: Svojstva zatvorenosti" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Regularni_jezik&amp;action=edit&amp;section=2" title="Uredi kôd odjeljka Svojstva zatvorenosti"><span>uredi kôd</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Regularni jezici su zatvoreni nad sljedećim operacijama: To jest, ako su <i>L</i> i <i>P</i> regularni jezici, tada su sljedeći jezici također regularni: </p> <ul><li>komplement <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 {\bar {L}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>L</mi> <mo stretchy="false">&#x00AF;<!-- ¯ --></mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\bar {L}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/693f7bc2de1da074453cc076992a69eb8d4a840a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.583ex; height:2.509ex;" alt="{\displaystyle {\bar {L}}}"></span> jezika <i>L</i></li> <li><a href="/wiki/Kleeneov_operator" title="Kleeneov operator">Kleeneov operator</a> <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 L^{*}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>&#x2217;<!-- ∗ --></mo> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L^{*}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d9a3547ba2f3cc5cb4463473815f227092b4766a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.637ex; height:2.343ex;" alt="{\displaystyle L^{*}}"></span> jezika <i>L</i></li> <li>slika (kodomena) <i>φ(L)</i> jezika <i>L</i> pod homeomorfizmom</li> <li>nadovezivanje (konkatenacija) <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 L\circ P}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>L</mi> <mo>&#x2218;<!-- ∘ --></mo> <mi>P</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L\circ P}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/eae46ff0ba4ad8c9e2b9cfab9f0b08ce37bd1581" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.523ex; height:2.176ex;" alt="{\displaystyle L\circ P}"></span> jezika <i>L</i> i <i>P</i></li> <li>unija <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 L\cup P}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>L</mi> <mo>&#x222A;<!-- ∪ --></mo> <mi>P</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L\cup P}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/09e9fef5be936343caeb70e10b5e9448b12705a9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.911ex; height:2.176ex;" alt="{\displaystyle L\cup P}"></span> jezika <i>L</i> i <i>P</i></li> <li>presjek <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 L\cap P}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>L</mi> <mo>&#x2229;<!-- ∩ --></mo> <mi>P</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L\cap P}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7ddfcbe07573129fe82433653ce72e025487c14f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.911ex; height:2.176ex;" alt="{\displaystyle L\cap P}"></span> jezika <i>L</i> i <i>P</i></li> <li>razlika <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 L-P}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>L</mi> <mo>&#x2212;<!-- − --></mo> <mi>P</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L-P}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7307b31a7222c63769f36164b281b1654f485aae" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:6.169ex; height:2.343ex;" alt="{\displaystyle L-P}"></span> jezika <i>L</i> i <i>P</i></li> <li>Prevrtanje <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 L^{R}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>R</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L^{R}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6fd88c02bc7694cf4fa03b53a085943fb6f3b862" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.062ex; height:2.676ex;" alt="{\displaystyle L^{R}}"></span> jezika <i>L</i></li> <li>POLOVICA(<i>L</i>), skup svih nizova znakova koji čine prvu polovicu nizova znakova u <i>L</i></li></ul> <div class="mw-heading mw-heading2"><h2 id="Odlučivanje_regularnosti_jezika"><span id="Odlu.C4.8Divanje_regularnosti_jezika"></span>Odlučivanje regularnosti jezika</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Regularni_jezik&amp;veaction=edit&amp;section=3" title="Uredi odlomak: Odlučivanje regularnosti jezika" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Regularni_jezik&amp;action=edit&amp;section=3" title="Uredi kôd odjeljka Odlučivanje regularnosti jezika"><span>uredi kôd</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Da bismo locirali regularne jezike u <a href="/wiki/Chomskyjeva_hijerarhija" title="Chomskyjeva hijerarhija">Chomskyjevoj hijerarhiji</a>, možemo prvo primijetiti da je svaki regularni jezik <a href="/wiki/Kontekstno_neovisni_jezik" title="Kontekstno neovisni jezik">kontekstno neovisan</a>. Obrat ne vrijedi: primjer je jezik koji sadrži jednak broj znakova <i>a</i> i <i>b</i>, koji je neregularan kontekstno neovisan jezik. Za dokaz neregularnosti jezika poput takvog može se koristiti <a href="/wiki/Myhill-Nerode_teorem" title="Myhill-Nerode teorem">Myhill-Nerode teorem</a> ili <a href="/wiki/Svojstvo_napuhavanja" title="Svojstvo napuhavanja">svojstvo napuhavanja</a>. </p><p>Postoje dva čisto algebarska pristupa prilikom definiranja regularnih jezika. Ako je &#931; konačna abeceda i &#931;* označava slobodni monoid nad &#931; ako se sastoji od svih nizova znakova nad &#931;, &#160;<i>f</i>&#160;: &#931;* &#8594; <i>M</i> je monoidni homeomorfizam pri čemu je <i>M</i> <i>konačni</i> monoid, <i>S</i> podskup skupa <i>M</i>, i pri tome je skup <i>f</i><sup>&#160;&#8722;1</sup>(<i>S</i>) regularan. Svaki regularni jezik može iznići na ovakav način. </p><p>Ako je <i>L</i> neki podskup skupa &#931;*, može se definirati relacija ekvivalencije ~ nad &#931;* na sljedeći način: <i>u</i> ~ <i>v</i> je definirana na način </p> <dl><dd><i>uw</i> &#8712; <i>L</i> ako i samo ako <i>vw</i> &#8712; <i>L</i> za svaki <i>w</i> &#8712; &#931;*</dd></dl> <p>Jezik <i>L</i> je regularan ako i samo ako broj klasa ekvivalencije relacije ~ je konačan. Ako je to istina, tada je taj broj jednak broju stanja minimalnog konačnog automata koji prihvaća <i>L</i>. </p> <div class="mw-heading mw-heading2"><h2 id="Konačni_jezici"><span id="Kona.C4.8Dni_jezici"></span>Konačni jezici</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Regularni_jezik&amp;veaction=edit&amp;section=4" title="Uredi odlomak: Konačni jezici" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Regularni_jezik&amp;action=edit&amp;section=4" title="Uredi kôd odjeljka Konačni jezici"><span>uredi kôd</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Konačni jezici su specifični podskup klase regularnih jezika - oni jezici koji sadrže samo konačan broj riječi. Oni su očito regularni jer se uvijek može napisati <a href="/wiki/Regularni_izraz" title="Regularni izraz">regularni izraz</a> koji je unija svih riječi u jeziku. </p> <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=Regularni_jezik&amp;veaction=edit&amp;section=5" title="Uredi odlomak: Izvori" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Regularni_jezik&amp;action=edit&amp;section=5" title="Uredi kôd odjeljka Izvori"><span>uredi kôd</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r6541845">.mw-parser-output .reflist{font-size:90%;margin-bottom:0.5em;list-style-type:decimal}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-InfoRjecnik-1"><span class="mw-cite-backlink"><a href="#cite_ref-InfoRjecnik_1-0">↑</a></span> <span class="reference-text">Kiš Miroslav, <i>Englesko-hrvatski i hrvatsko-engleski informatički rječnik</i>, Zagreb, Naklada Ljevak, 2000., str. 785</span> </li> </ol></div></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="CITEREFMichael_Sipser1997" class="citation book cs1"><a href="/w/index.php?title=Michael_Sipser&amp;action=edit&amp;redlink=1" class="new" title="Michael Sipser (stranica ne postoji)">Michael Sipser</a>. 1997. <i>Introduction to the Theory of Computation</i>. PWS Publishing. <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/0-534-94728-X" title="Posebno:Traži ISBN/0-534-94728-X">0-534-94728-X</a></cite><span title="ctx_ver=Z39.88-2004&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&amp;rft.genre=book&amp;rft.btitle=Introduction+to+the+Theory+of+Computation&amp;rft.pub=PWS+Publishing&amp;rft.date=1997&amp;rft.au=Michael+Sipser&amp;rfr_id=info%3Asid%2Fhr.wikipedia.org%3ARegularni+jezik" class="Z3988"></span></li></ul> <ul><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&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&amp;rft.genre=book&amp;rft.btitle=Jezi%C4%8Dni+procesori+1&amp;rft.pub=Element&amp;rft.date=2003&amp;rft.au=Sini%C5%A1a+Srblji%C4%87&amp;rfr_id=info%3Asid%2Fhr.wikipedia.org%3ARegularni+jezik" 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=Regularni_jezik&amp;veaction=edit&amp;section=6" 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=Regularni_jezik&amp;action=edit&amp;section=6" title="Uredi kôd odjeljka Vanjske poveznice"><span>uredi kôd</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>Odsjek za računarstvo na University of Western Ontario: <i>Grail+</i>, <a rel="nofollow" class="external free" href="http://www.csd.uwo.ca/Research/grail/">http://www.csd.uwo.ca/Research/grail/</a> &#8194;<a rel="nofollow" class="external text" href="https://web.archive.org/web/20060404094049/http://www.csd.uwo.ca/Research/grail/">Arhivirana inačica izvorne stranice</a>&#32;od 4. travnja 2006. (<a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>). Programski paket za manipuliranje regularnim izrazima, konačnim automatima i konačnim jezicima. Besplatan za nekomercijalnu uporabu.</li> <li>Chalchalero! <a rel="nofollow" class="external free" href="http://www.ucse.edu.ar/fma/sepa/chalchalero.htm">http://www.ucse.edu.ar/fma/sepa/chalchalero.htm</a> &#8194;<a rel="nofollow" class="external text" href="https://web.archive.org/web/20070118144136/http://www.ucse.edu.ar/fma/sepa/chalchalero.htm">Arhivirana inačica izvorne stranice</a>&#32;od 18. siječnja 2007. (<a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>). Besplatan vizualni softver za manipulaciju regularnim izrazima, regularnim gramatikama, konačnim automatima i konačnim jezicima razvijen od strane projekta SEPa! (Universidad Católica de Santiago del Estero)</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 href="/wiki/Chomskyjeva_hijerarhija" title="Chomskyjeva hijerarhija">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&amp;action=edit&amp;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 class="mw-selflink selflink">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> <!-- NewPP limit report Parsed by mw‐web.eqiad.main‐559c9fd9f4‐vns5v Cached time: 20241126132147 Cache expiry: 2592000 Reduced expiry: false Complications: [vary‐revision‐sha1, show‐toc] CPU time usage: 0.129 seconds Real time usage: 0.209 seconds Preprocessor visited node count: 372/1000000 Post‐expand include size: 6316/2097152 bytes Template argument size: 782/2097152 bytes Highest expansion depth: 10/100 Expensive parser function count: 0/500 Unstrip recursion depth: 0/20 Unstrip post‐expand size: 5571/5000000 bytes Lua time usage: 0.063/10.000 seconds Lua memory usage: 2707195/52428800 bytes Number of Wikibase entities loaded: 0/400 --> <!-- Transclusion expansion time report (%,ms,calls,template) 100.00% 130.006 1 -total 79.15% 102.902 2 Predložak:Cite_book 10.06% 13.077 1 Predložak:Izvori 6.67% 8.667 2 Predložak:Webarchive 5.80% 7.544 2 Predložak:ISBN 3.71% 4.825 1 Predložak:Formalni_jezici_i_gramatike 3.25% 4.224 2 Predložak:DatumFormat 1.27% 1.645 2 Predložak:If_then_show 1.12% 1.458 2 Predložak:Void --> <!-- Saved in parser cache with key hrwiki:pcache:75204:|#|:idhash:canonical and timestamp 20241126132147 and revision id 6004939. 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