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Classe di complessità - Wikipedia

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<h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Classe di complessità</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="Vai a una voce in un&#039;altra lingua. 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href="https://ca.wikipedia.org/wiki/Classe_de_complexitat" title="Classe de complexitat - catalano" lang="ca" hreflang="ca" data-title="Classe de complexitat" data-language-autonym="Català" data-language-local-name="catalano" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Komplexit%C3%A4tsklasse" title="Komplexitätsklasse - tedesco" lang="de" hreflang="de" data-title="Komplexitätsklasse" data-language-autonym="Deutsch" data-language-local-name="tedesco" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Complexity_class" title="Complexity class - inglese" lang="en" hreflang="en" data-title="Complexity class" data-language-autonym="English" data-language-local-name="inglese" 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/Clase_de_complejidad" title="Clase de complejidad - spagnolo" lang="es" hreflang="es" data-title="Clase de complejidad" data-language-autonym="Español" data-language-local-name="spagnolo" 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/%DA%A9%D9%84%D8%A7%D8%B3_%D9%BE%DB%8C%DA%86%DB%8C%D8%AF%DA%AF%DB%8C" title="کلاس پیچیدگی - persiano" lang="fa" hreflang="fa" data-title="کلاس پیچیدگی" data-language-autonym="فارسی" data-language-local-name="persiano" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Classe_de_complexit%C3%A9" title="Classe de complexité - francese" lang="fr" hreflang="fr" data-title="Classe de complexité" data-language-autonym="Français" data-language-local-name="francese" 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%9E%D7%97%D7%9C%D7%A7%D7%AA_%D7%A1%D7%99%D7%91%D7%95%D7%9B%D7%99%D7%95%D7%AA" title="מחלקת סיבוכיות - ebraico" lang="he" hreflang="he" data-title="מחלקת סיבוכיות" data-language-autonym="עברית" data-language-local-name="ebraico" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Klasa_slo%C5%BEenosti" title="Klasa složenosti - croato" lang="hr" hreflang="hr" data-title="Klasa složenosti" data-language-autonym="Hrvatski" data-language-local-name="croato" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E8%A4%87%E9%9B%91%E6%80%A7%E3%82%AF%E3%83%A9%E3%82%B9" title="複雑性クラス - giapponese" lang="ja" hreflang="ja" data-title="複雑性クラス" data-language-autonym="日本語" data-language-local-name="giapponese" 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/%EB%B3%B5%EC%9E%A1%EB%8F%84_%EC%A2%85%EB%A5%98" title="복잡도 종류 - coreano" lang="ko" hreflang="ko" data-title="복잡도 종류" data-language-autonym="한국어" data-language-local-name="coreano" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Complexiteitsgraad" title="Complexiteitsgraad - olandese" lang="nl" hreflang="nl" data-title="Complexiteitsgraad" data-language-autonym="Nederlands" data-language-local-name="olandese" 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/Kompleksitetsklasse" title="Kompleksitetsklasse - norvegese nynorsk" lang="nn" hreflang="nn" data-title="Kompleksitetsklasse" data-language-autonym="Norsk nynorsk" data-language-local-name="norvegese 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/Kompleksitetsklasse" title="Kompleksitetsklasse - norvegese bokmål" lang="nb" hreflang="nb" data-title="Kompleksitetsklasse" data-language-autonym="Norsk bokmål" data-language-local-name="norvegese 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/Klasa_z%C5%82o%C5%BCono%C5%9Bci" title="Klasa złożoności - polacco" lang="pl" hreflang="pl" data-title="Klasa złożoności" data-language-autonym="Polski" data-language-local-name="polacco" 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/Classe_de_complexidade" title="Classe de complexidade - portoghese" lang="pt" hreflang="pt" data-title="Classe de complexidade" data-language-autonym="Português" data-language-local-name="portoghese" 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/Clas%C4%83_de_complexitate" title="Clasă de complexitate - rumeno" lang="ro" hreflang="ro" data-title="Clasă de complexitate" data-language-autonym="Română" data-language-local-name="rumeno" 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%9A%D0%BB%D0%B0%D1%81%D1%81_%D1%81%D0%BB%D0%BE%D0%B6%D0%BD%D0%BE%D1%81%D1%82%D0%B8" title="Класс сложности - russo" lang="ru" hreflang="ru" data-title="Класс сложности" data-language-autonym="Русский" data-language-local-name="russo" 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/Klasa_slo%C5%BEenosti" title="Klasa složenosti - serbo-croato" lang="sh" hreflang="sh" data-title="Klasa složenosti" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="serbo-croato" 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/Complexity_class" title="Complexity class - Simple English" lang="en-simple" hreflang="en-simple" data-title="Complexity class" 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-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%9A%D0%BB%D0%B0%D1%81%D0%B0_%D1%81%D0%BB%D0%BE%D0%B6%D0%B5%D0%BD%D0%BE%D1%81%D1%82%D0%B8" title="Класа сложености - serbo" lang="sr" hreflang="sr" data-title="Класа сложености" data-language-autonym="Српски / srpski" data-language-local-name="serbo" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Komplexitetsklass" title="Komplexitetsklass - svedese" lang="sv" hreflang="sv" data-title="Komplexitetsklass" data-language-autonym="Svenska" data-language-local-name="svedese" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E8%A4%87%E9%9B%9C%E5%BA%A6%E9%A1%9E" title="複雜度類 - cinese" lang="zh" hreflang="zh" data-title="複雜度類" data-language-autonym="中文" data-language-local-name="cinese" 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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">Aspetto</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">sposta nella barra laterale</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">nascondi</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">Da Wikipedia, l&#039;enciclopedia libera.</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="it" dir="ltr"><figure typeof="mw:File/Thumb"><a href="/wiki/File:Complexity_subsets_pspace.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6e/Complexity_subsets_pspace.svg/300px-Complexity_subsets_pspace.svg.png" decoding="async" width="300" height="273" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6e/Complexity_subsets_pspace.svg/450px-Complexity_subsets_pspace.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6e/Complexity_subsets_pspace.svg/600px-Complexity_subsets_pspace.svg.png 2x" data-file-width="485" data-file-height="441" /></a><figcaption>Rappresentazione delle varie classi di complessità</figcaption></figure> <p>Nella <a href="/wiki/Teoria_della_complessit%C3%A0_computazionale" title="Teoria della complessità computazionale">teoria della complessità computazionale</a>, una <b>classe di complessità</b> è un <a href="/wiki/Insieme" title="Insieme">insieme</a> di <a href="/wiki/Problema_computazionale" title="Problema computazionale">problemi</a> di una certa complessità. Un esempio tipico di definizione di classe di complessità ha la forma: </p> <dl><dd>l'insieme di problemi che, se esiste la soluzione, possono essere risolti da una <a href="/wiki/Macchina_astratta" title="Macchina astratta">macchina astratta</a> M usando <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 O(f(n))}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>O</mi> <mo stretchy="false">(</mo> <mi>f</mi> <mo stretchy="false">(</mo> <mi>n</mi> <mo stretchy="false">)</mo> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle O(f(n))}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/756b4d8648334719f65bf5e6269c7a2b3a502f13" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:8.065ex; height:2.843ex;" alt="{\displaystyle O(f(n))}"></span> della risorsa R, con <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> dimensione dell'input</dd></dl> <p>Ad esempio, la classe <a href="/wiki/NP_(complessit%C3%A0)" title="NP (complessità)">NP</a> è l'insieme dei problemi di decisione che possono essere risolti da una <a href="/wiki/Macchina_di_Turing#Macchina_di_Turing_non_deterministica" title="Macchina di Turing">macchina di Turing non deterministica</a> in tempo polinomiale, mentre la classe <a href="/wiki/P_(complessit%C3%A0)" title="P (complessità)">P</a> è l'insieme dei problemi di decisione che possono essere risolti da una <a href="/wiki/Macchina_di_Turing" title="Macchina di Turing">macchina di Turing</a> deterministica in tempo polinomiale. Alcune classi di complessità sono insiemi di problemi costruttivi (cioè che richiedono di calcolare una funzione, e non di rispondere SÌ o NO), come ad esempio <a href="/w/index.php?title=FP_(complessit%C3%A0)&amp;action=edit&amp;redlink=1" class="new" title="FP (complessità) (la pagina non esiste)">FP</a>. </p><p>Molte classi di complessità possono essere caratterizzate in termini della <a href="/wiki/Logica_matematica" title="Logica matematica">logica matematica</a> necessaria ad esprimerle; vedi <a href="/w/index.php?title=Complessit%C3%A0_descrittiva&amp;action=edit&amp;redlink=1" class="new" title="Complessità descrittiva (la pagina non esiste)">complessità descrittiva</a>. </p><p>Gli <a href="/w/index.php?title=Assiomi_di_Blum&amp;action=edit&amp;redlink=1" class="new" title="Assiomi di Blum (la pagina non esiste)">assiomi di Blum</a> possono essere usati per definire classi di complessità senza riferirsi ad un <a href="/w/index.php?title=Modello_computazionale&amp;action=edit&amp;redlink=1" class="new" title="Modello computazionale (la pagina non esiste)">modello computazionale</a> concreto. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Relazioni_tra_classi_di_complessità"><span id="Relazioni_tra_classi_di_complessit.C3.A0"></span>Relazioni tra classi di complessità</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Classe_di_complessit%C3%A0&amp;veaction=edit&amp;section=1" title="Modifica la sezione Relazioni tra classi di complessità" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Classe_di_complessit%C3%A0&amp;action=edit&amp;section=1" title="Edit section&#039;s source code: Relazioni tra classi di complessità"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>La seguente tabella mostra alcune classi di problemi (o di linguaggi) che sono considerate nella teoria della complessità. Se la classe <b>X</b> è un <a href="/wiki/Sottoinsieme" class="mw-redirect" title="Sottoinsieme">sottoinsieme</a> stretto di <b>Y</b>, allora <b>X</b> è rappresentata sotto ad <b>Y</b>, con una linea continua che li connette. Se <b>X</b> è un sottoinsieme, ma non si sa se <b>X</b> e <b>Y</b> sono insiemi uguali, allora la linea è tratteggiata. Tecnicamente, la suddivisione tra problemi solubili e insolubili appartiene più alla <a href="/wiki/Teoria_della_calcolabilit%C3%A0" title="Teoria della calcolabilità">teoria della calcolabilità</a>, ma aiuta a vedere in prospettiva le classi di complessità. </p> <table cellpadding="0" cellspacing="0" border="0" align="center"> <tbody><tr align="center"> <td colspan="2"> </td> <td colspan="4"> <table cellpadding="0" cellspacing="0" border="1" bgcolor="lightBlue" width="100%"> <tbody><tr> <td align="center"><a href="/wiki/Problema_decisionale" title="Problema decisionale">Problemi di decisione</a> </td></tr></tbody></table> </td></tr> <tr align="center"> <td colspan="2"> </td> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/File:SolidLine.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/2/2d/SolidLine.png" decoding="async" width="4" height="40" class="mw-file-element" data-file-width="4" data-file-height="40" /></a></span> </td> <td colspan="2"> </td> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/File:SolidLine.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/2/2d/SolidLine.png" decoding="async" width="4" height="40" class="mw-file-element" data-file-width="4" data-file-height="40" /></a></span> </td></tr> <tr align="center"> <td colspan="3"> <table cellpadding="0" cellspacing="0" border="1" bgcolor="lightBlue" width="100%"> <tbody><tr> <td align="center"><a href="/wiki/Linguaggio_ricorsivamente_enumerabile" title="Linguaggio ricorsivamente enumerabile">Tipo 0 (Ricorsivamente enumerabili)</a> </td></tr></tbody></table> </td> <td> </td> <td colspan="4"> <table cellpadding="0" cellspacing="0" border="1" bgcolor="lightBlue" width="100%"> <tbody><tr> <td align="center"><a href="/wiki/Problema_decisionale" title="Problema decisionale">Indecidibili</a> </td></tr></tbody></table> </td></tr> <tr align="center"> <td colspan="3"><span class="mw-default-size" typeof="mw:File"><a href="/wiki/File:SolidLine.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/2/2d/SolidLine.png" decoding="async" width="4" height="40" class="mw-file-element" data-file-width="4" data-file-height="40" /></a></span> </td></tr> <tr align="center"> <td colspan="3"> <table cellpadding="0" cellspacing="0" border="1" bgcolor="lightBlue" width="100%"> <tbody><tr> <td align="center"><a href="/wiki/Linguaggio_ricorsivo" title="Linguaggio ricorsivo">Decidibile</a> </td></tr></tbody></table> </td></tr> <tr align="center"> <td colspan="3"><span class="mw-default-size" typeof="mw:File"><a href="/wiki/File:SolidLine.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/2/2d/SolidLine.png" decoding="async" width="4" height="40" class="mw-file-element" data-file-width="4" data-file-height="40" /></a></span> </td></tr> <tr align="center"> <td colspan="3"> <table cellpadding="0" cellspacing="0" border="1" bgcolor="lightGreen" width="100%"> <tbody><tr> <td align="center"><a href="/wiki/EXPSPACE" title="EXPSPACE">EXPSPACE</a> </td></tr></tbody></table> </td></tr> <tr align="center"> <td colspan="3"><span class="mw-default-size" typeof="mw:File"><a href="/wiki/File:DottedLine.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/DottedLine.png" decoding="async" width="4" height="40" class="mw-file-element" data-file-width="4" data-file-height="40" /></a></span> </td></tr> <tr align="center"> <td colspan="3"> <table cellpadding="0" cellspacing="0" border="1" bgcolor="lightGreen" width="100%"> <tbody><tr> <td align="center"><a href="/wiki/EXPTIME" title="EXPTIME">EXPTIME</a> </td></tr></tbody></table> </td></tr> <tr align="center"> <td colspan="3"><span class="mw-default-size" typeof="mw:File"><a href="/wiki/File:DottedLine.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/DottedLine.png" decoding="async" width="4" height="40" class="mw-file-element" data-file-width="4" data-file-height="40" /></a></span> </td></tr> <tr align="center"> <td colspan="8"> <table cellpadding="0" cellspacing="0" border="1" bgcolor="lightGreen" width="100%"> <tbody><tr> <td align="center"><a href="/wiki/PSPACE" title="PSPACE">PSPACE</a> </td></tr></tbody></table> </td></tr> <tr align="center"> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/File:SolidLine.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/2/2d/SolidLine.png" decoding="async" width="4" height="40" class="mw-file-element" data-file-width="4" data-file-height="40" /></a></span> </td> <td width="40"><span class="mw-default-size" typeof="mw:File"><a href="/wiki/File:SolidLine.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/2/2d/SolidLine.png" decoding="async" width="4" height="40" class="mw-file-element" data-file-width="4" data-file-height="40" /></a></span> </td> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/File:DottedLine.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/DottedLine.png" decoding="async" width="4" height="40" class="mw-file-element" data-file-width="4" data-file-height="40" /></a></span> </td> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/File:DottedLine.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/DottedLine.png" decoding="async" width="4" height="40" class="mw-file-element" data-file-width="4" data-file-height="40" /></a></span> </td> <td> </td> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/File:DottedLine.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/DottedLine.png" decoding="async" width="4" height="40" class="mw-file-element" data-file-width="4" data-file-height="40" /></a></span> </td> <td> </td> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/File:DottedLine.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/DottedLine.png" decoding="async" width="4" height="40" class="mw-file-element" data-file-width="4" data-file-height="40" /></a></span> </td></tr> <tr align="center"> <td> <table cellpadding="0" cellspacing="0" border="1" bgcolor="lightBlue" width="100%"> <tbody><tr> <td align="center"><a href="/wiki/Linguaggio_dipendente_dal_contesto" title="Linguaggio dipendente dal contesto">Tipo 1 (dipendente dal contesto)</a> </td></tr></tbody></table> </td> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/File:SolidLine.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/2/2d/SolidLine.png" decoding="async" width="4" height="40" class="mw-file-element" data-file-width="4" data-file-height="40" /></a></span> </td> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/File:DottedLine.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/DottedLine.png" decoding="async" width="4" height="40" class="mw-file-element" data-file-width="4" data-file-height="40" /></a></span> </td> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/File:DottedLine.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/DottedLine.png" decoding="async" width="4" height="40" class="mw-file-element" data-file-width="4" data-file-height="40" /></a></span> </td> <td> </td> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/File:DottedLine.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/DottedLine.png" decoding="async" width="4" height="40" class="mw-file-element" data-file-width="4" data-file-height="40" /></a></span> </td> <td> </td> <td colspan="1"> <table cellpadding="0" cellspacing="0" border="1" bgcolor="lightGreen" width="100%"> <tbody><tr> <td 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src="//upload.wikimedia.org/wikipedia/commons/2/2d/SolidLine.png" decoding="async" width="4" height="40" class="mw-file-element" data-file-width="4" data-file-height="40" /></a></span> </td> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/File:SolidLine.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/2/2d/SolidLine.png" decoding="async" width="4" height="40" class="mw-file-element" data-file-width="4" data-file-height="40" /></a></span> </td> <td> <table cellpadding="0" cellspacing="0" border="1" bgcolor="lightGreen" width="100%"> <tbody><tr> <td align="center"><a href="/wiki/Co-NP" title="Co-NP">Co-NP</a> </td></tr></tbody></table> </td> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/File:DottedLine.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/DottedLine.png" decoding="async" width="4" height="40" class="mw-file-element" data-file-width="4" data-file-height="40" /></a></span> </td> <td> </td> <td colspan="3"> <table cellpadding="0" cellspacing="0" border="1" bgcolor="lightGreen" width="100%"> <tbody><tr> <td align="center"><a href="/wiki/NP_(complessit%C3%A0)" title="NP (complessità)">NP</a> </td></tr></tbody></table> </td></tr> <tr align="center"> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/File:SolidLine.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/2/2d/SolidLine.png" decoding="async" width="4" height="40" class="mw-file-element" data-file-width="4" data-file-height="40" /></a></span> </td> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/File:SolidLine.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/2/2d/SolidLine.png" decoding="async" width="4" height="40" class="mw-file-element" data-file-width="4" data-file-height="40" /></a></span> </td> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/File:DottedLine.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/DottedLine.png" decoding="async" width="4" height="40" class="mw-file-element" data-file-width="4" data-file-height="40" /></a></span> </td> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/File:DottedLine.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/DottedLine.png" decoding="async" width="4" height="40" class="mw-file-element" data-file-width="4" data-file-height="40" /></a></span> </td> <td> </td> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/File:DottedLine.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/DottedLine.png" decoding="async" width="4" height="40" class="mw-file-element" data-file-width="4" data-file-height="40" /></a></span> </td> <td> </td> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/File:DottedLine.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/DottedLine.png" decoding="async" width="4" height="40" class="mw-file-element" data-file-width="4" data-file-height="40" /></a></span> </td></tr> <tr align="center"> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/File:SolidLine.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/2/2d/SolidLine.png" decoding="async" width="4" height="40" class="mw-file-element" data-file-width="4" data-file-height="40" /></a></span> </td> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/File:SolidLine.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/2/2d/SolidLine.png" decoding="async" width="4" height="40" class="mw-file-element" data-file-width="4" data-file-height="40" /></a></span> </td> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/File:DottedLine.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/DottedLine.png" decoding="async" width="4" height="40" class="mw-file-element" data-file-width="4" data-file-height="40" /></a></span> </td> <td> <table cellpadding="0" cellspacing="0" border="1" bgcolor="lightGreen" width="100%"> <tbody><tr> <td align="center"><a href="/wiki/BPP_(complessit%C3%A0)" title="BPP (complessità)">BPP</a> </td></tr></tbody></table> </td> <td width="10"> </td> <td> <table cellpadding="0" cellspacing="0" border="1" bgcolor="lightGreen" width="100%"> <tbody><tr> <td align="center"><a href="/wiki/BQP_(complessit%C3%A0)" title="BQP (complessità)">BQP</a> </td></tr></tbody></table> </td> <td width="10"> </td> <td> <table cellpadding="0" cellspacing="0" border="1" bgcolor="lightGreen" width="100%"> <tbody><tr> <td align="center"><a href="/wiki/NP-Completo" class="mw-redirect" title="NP-Completo">NP-Completi</a> </td></tr></tbody></table> </td></tr> <tr align="center"> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/File:SolidLine.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/2/2d/SolidLine.png" decoding="async" width="4" height="40" class="mw-file-element" data-file-width="4" data-file-height="40" /></a></span> </td> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/File:SolidLine.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/2/2d/SolidLine.png" decoding="async" width="4" height="40" class="mw-file-element" data-file-width="4" data-file-height="40" /></a></span> </td> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/File:DottedLine.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/c/c7/DottedLine.png" decoding="async" width="4" height="40" class="mw-file-element" data-file-width="4" data-file-height="40" /></a></span> </td> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/File:DottedLine.png" 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class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/2/2d/SolidLine.png" decoding="async" width="4" height="40" class="mw-file-element" data-file-width="4" data-file-height="40" /></a></span> </td> <td colspan="6"> <table cellpadding="0" cellspacing="0" border="1" bgcolor="lightGreen" width="100%"> <tbody><tr> <td align="center"><a href="/wiki/P_(complessit%C3%A0)" title="P (complessità)">P</a> </td></tr></tbody></table> </td></tr> <tr align="center"> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/File:SolidLine.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/2/2d/SolidLine.png" decoding="async" width="4" height="40" class="mw-file-element" data-file-width="4" data-file-height="40" /></a></span> </td> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/File:SolidLine.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/2/2d/SolidLine.png" decoding="async" 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height="40" class="mw-file-element" data-file-width="4" data-file-height="40" /></a></span> </td> <td colspan="2"> <table cellpadding="0" cellspacing="0" border="1" bgcolor="lightGreen" width="100%"> <tbody><tr> <td align="center"><a href="/wiki/NC_(complessit%C3%A0)" title="NC (complessità)">NC</a> </td></tr></tbody></table> </td> <td colspan="4"> </td> <td> <table cellpadding="0" cellspacing="0" border="1" bgcolor="lightGreen" width="100%"> <tbody><tr> <td align="center"><a href="/w/index.php?title=P-Completo&amp;action=edit&amp;redlink=1" class="new" title="P-Completo (la pagina non esiste)">P-Completi</a> </td></tr></tbody></table> </td></tr> <tr align="center"> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/File:SolidLine.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/2/2d/SolidLine.png" decoding="async" width="4" height="40" class="mw-file-element" data-file-width="4" data-file-height="40" /></a></span> </td> <td colspan="2"><span class="mw-default-size" typeof="mw:File"><a href="/wiki/File:SolidLine.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/2/2d/SolidLine.png" decoding="async" width="4" height="40" class="mw-file-element" data-file-width="4" data-file-height="40" /></a></span> </td></tr> <tr align="center"> <td colspan="3"> <table cellpadding="0" cellspacing="0" border="1" bgcolor="lightBlue" width="100%"> <tbody><tr> <td align="center"><a href="/wiki/Linguaggio_libero_dal_contesto" title="Linguaggio libero dal contesto">Tipo 2 (libero dal contesto)</a> </td></tr></tbody></table> </td></tr> <tr align="center"> <td colspan="3"><span class="mw-default-size" typeof="mw:File"><a href="/wiki/File:SolidLine.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/2/2d/SolidLine.png" decoding="async" width="4" height="40" class="mw-file-element" data-file-width="4" data-file-height="40" /></a></span> </td></tr> <tr align="center"> <td colspan="3"> <table cellpadding="0" cellspacing="0" border="1" bgcolor="lightBlue" width="100%"> <tbody><tr> <td align="center"><a href="/wiki/Linguaggio_regolare" title="Linguaggio regolare">Tipo 3 (Regolare)</a> </td></tr></tbody></table> </td></tr></tbody></table> <div class="mw-heading mw-heading2"><h2 id="Bibliografia">Bibliografia</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Classe_di_complessit%C3%A0&amp;veaction=edit&amp;section=2" title="Modifica la sezione Bibliografia" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Classe_di_complessit%C3%A0&amp;action=edit&amp;section=2" title="Edit section&#039;s source code: Bibliografia"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20100726082118/http://qwiki.stanford.edu/wiki/Complexity_Zoo">The Complexity Zoo</a>: una lista di classi di complessità, come riferimento per gli esperti.</li> <li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20160416021243/https://people.cs.umass.edu/~immerman/complexity_theory.html">Diagram</a> by <a href="/w/index.php?title=Neil_Immerman&amp;action=edit&amp;redlink=1" class="new" title="Neil Immerman (la pagina non esiste)">Neil Immerman</a> mostra la gerarchia delle classi di complessità e come queste si combinano tra di loro.</li> <li><a href="/w/index.php?title=Garey,_Michael_R.&amp;action=edit&amp;redlink=1" class="new" title="Garey, Michael R. (la pagina non esiste)">Michael Garey</a>, and <a href="/wiki/David_S._Johnson" title="David S. Johnson">David S. Johnson</a>: <i>Computers and Intractability: A Guide to the Theory of NP-Completeness.</i> New York: W. H. Freeman &amp; Co., 1979. Il riferimento standard per i problemi <a href="/wiki/NP-Completo" class="mw-redirect" title="NP-Completo">NP-Completi</a>.</li></ul> <div class="mw-heading mw-heading2"><h2 id="Voci_correlate">Voci correlate</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Classe_di_complessit%C3%A0&amp;veaction=edit&amp;section=3" title="Modifica la sezione Voci correlate" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Classe_di_complessit%C3%A0&amp;action=edit&amp;section=3" title="Edit section&#039;s source code: Voci correlate"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Lista_delle_classi_di_complessit%C3%A0" title="Lista delle classi di complessità">Lista delle classi di complessità</a></li> <li><a href="/wiki/Teoria_della_calcolabilit%C3%A0" title="Teoria della calcolabilità">Teoria della calcolabilità</a></li> <li><a href="/wiki/Teoria_della_complessit%C3%A0_computazionale" title="Teoria della complessità computazionale">Teoria della complessità computazionale</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Collegamenti_esterni">Collegamenti esterni</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Classe_di_complessit%C3%A0&amp;veaction=edit&amp;section=4" title="Modifica la sezione Collegamenti esterni" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Classe_di_complessit%C3%A0&amp;action=edit&amp;section=4" title="Edit section&#039;s source code: Collegamenti esterni"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><cite id="CITEREFFOLDOC" class="citation testo" style="font-style:normal">(<span style="font-weight:bolder; font-size:80%"><abbr title="inglese">EN</abbr></span>) Denis Howe, <span style="font-style:italic;"><a href="https://foldoc.org/complexity_class" class="extiw" title="foldoc:complexity class">complexity class</a></span>, in <span style="font-style:italic;"><a href="/wiki/Free_On-line_Dictionary_of_Computing" title="Free On-line Dictionary of Computing">Free On-line Dictionary of Computing</a></span>.</cite> Disponibile con licenza <a href="/wiki/GNU_Free_Documentation_License" title="GNU Free Documentation License">GFDL</a></li></ul> <style data-mw-deduplicate="TemplateStyles:r141815314">.mw-parser-output .navbox{border:1px solid #aaa;clear:both;margin:auto;padding:2px;width:100%}.mw-parser-output .navbox th{padding-left:1em;padding-right:1em;text-align:center}.mw-parser-output .navbox>tbody>tr:first-child>th{background:#ccf;font-size:90%;width:100%;color:var(--color-base,black)}.mw-parser-output .navbox_navbar{float:left;margin:0;padding:0 10px 0 0;text-align:left;width:6em}.mw-parser-output .navbox_title{font-size:110%}.mw-parser-output .navbox_abovebelow{background:#ddf;font-size:90%;font-weight:normal}.mw-parser-output .navbox_group{background:#ddf;font-size:90%;padding:0 10px;white-space:nowrap}.mw-parser-output .navbox_list{font-size:90%;width:100%}.mw-parser-output .navbox_list a{white-space:nowrap}html:not(.vector-feature-night-mode-enabled) .mw-parser-output .navbox_odd{background:#fdfdfd;color:var(--color-base,black)}html:not(.vector-feature-night-mode-enabled) .mw-parser-output .navbox_even{background:#f7f7f7;color:var(--color-base,black)}.mw-parser-output .navbox a.mw-selflink{color:var(--color-base,black)}.mw-parser-output .navbox_center{text-align:center}.mw-parser-output .navbox .navbox_image{padding-left:7px;vertical-align:middle;width:0}.mw-parser-output .navbox+.navbox{margin-top:-1px}.mw-parser-output .navbox .mw-collapsible-toggle{font-weight:normal;text-align:right;width:7em}body.skin--responsive .mw-parser-output .navbox_image img{max-width:none!important}.mw-parser-output .subnavbox{margin:-3px;width:100%}.mw-parser-output .subnavbox_group{background:#e6e6ff;padding:0 10px}@media screen{html.skin-theme-clientpref-night .mw-parser-output .navbox>tbody>tr:first-child>th{background:var(--background-color-interactive)!important}html.skin-theme-clientpref-night .mw-parser-output .navbox th{color:var(--color-base)!important}html.skin-theme-clientpref-night .mw-parser-output .navbox_abovebelow,html.skin-theme-clientpref-night .mw-parser-output .navbox_group{background:var(--background-color-interactive-subtle)!important}html.skin-theme-clientpref-night .mw-parser-output .subnavbox_group{background:var(--background-color-neutral-subtle)!important}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .navbox>tbody>tr:first-child>th{background:var(--background-color-interactive)!important}html.skin-theme-clientpref-os .mw-parser-output .navbox th{color:var(--color-base)!important}html.skin-theme-clientpref-os .mw-parser-output .navbox_abovebelow,html.skin-theme-clientpref-os .mw-parser-output .navbox_group{background:var(--background-color-interactive-subtle)!important}html.skin-theme-clientpref-os .mw-parser-output .subnavbox_group{background:var(--background-color-neutral-subtle)!important}}</style><table class="navbox mw-collapsible autocollapse noprint metadata" id="navbox-Classi_di_complessità"><tbody><tr><th colspan="2"><div class="navbox_navbar"><div class="noprint plainlinks" style="background-color:transparent; 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Usa l&#39;anteprima prima di salvare">M</span></a></div></div><span class="navbox_title"><a class="mw-selflink selflink">Classi di complessità</a> (<a href="/wiki/Lista_delle_classi_di_complessit%C3%A0" title="Lista delle classi di complessità">elenco</a>)</span></th></tr><tr><td colspan="2" class="navbox_list navbox_center navbox_odd"><a href="/wiki/P_(complessit%C3%A0)" title="P (complessità)">P</a><b>&#160;·</b> <a href="/wiki/NP_(complessit%C3%A0)" title="NP (complessità)">NP</a><b>&#160;·</b> <a href="/wiki/Co-NP" title="Co-NP">co-NP</a><b>&#160;·</b> <a href="/wiki/NP-completo" title="NP-completo">NP-C</a><b>&#160;·</b> <a href="/wiki/Co-NP-completo" title="Co-NP-completo">co-NP-C</a><b>&#160;·</b> <a href="/wiki/NP-difficile" title="NP-difficile">NP-hard</a><b>&#160;·</b> <a href="/w/index.php?title=UP_(complessit%C3%A0)&amp;action=edit&amp;redlink=1" class="new" title="UP (complessità) (la pagina non esiste)">UP</a><b>&#160;·</b> <a href="/wiki/Sharp-P" title="Sharp-P">#P</a><b>&#160;·</b> <a href="/wiki/Sharp-P-completo" title="Sharp-P-completo">#P-C</a><b>&#160;·</b> <a href="/wiki/L_(complessit%C3%A0)" title="L (complessità)">L</a><b>&#160;·</b> <a href="/wiki/NL_(complessit%C3%A0)" title="NL (complessità)">NL</a><b>&#160;·</b> <a href="/wiki/NC_(complessit%C3%A0)" title="NC (complessità)">NC</a><b>&#160;·</b> <a href="/w/index.php?title=P-completo&amp;action=edit&amp;redlink=1" class="new" title="P-completo (la pagina non esiste)">P-C</a><b>&#160;·</b> <a href="/wiki/PSPACE" title="PSPACE">PSPACE</a><b>&#160;·</b> <a href="/wiki/PSPACE-completo" title="PSPACE-completo">PSPACE-C</a><b>&#160;·</b> <a href="/wiki/EXPTIME" title="EXPTIME">EXPTIME</a><b>&#160;·</b> <a href="/wiki/EXPSPACE" title="EXPSPACE">EXPSPACE</a><b>&#160;·</b> <a href="/w/index.php?title=PR_(complessit%C3%A0)&amp;action=edit&amp;redlink=1" class="new" title="PR (complessità) (la pagina non esiste)">PR</a><b>&#160;·</b> <a href="/w/index.php?title=RE_(complessit%C3%A0)&amp;action=edit&amp;redlink=1" class="new" title="RE (complessità) (la pagina non esiste)">RE</a><b>&#160;·</b> <a href="/w/index.php?title=Co-RE&amp;action=edit&amp;redlink=1" class="new" title="Co-RE (la pagina non esiste)">Co-RE</a><b>&#160;·</b> <a href="/w/index.php?title=RE-completo&amp;action=edit&amp;redlink=1" class="new" title="RE-completo (la pagina non esiste)">RE-C</a><b>&#160;·</b> <a href="/w/index.php?title=Co-RE-completo&amp;action=edit&amp;redlink=1" class="new" title="Co-RE-completo (la pagina non esiste)">Co-RE-C</a><b>&#160;·</b> <a href="/w/index.php?title=R_(complessit%C3%A0)&amp;action=edit&amp;redlink=1" class="new" title="R (complessità) (la pagina non esiste)">R</a><b>&#160;·</b> <a href="/wiki/BQP_(complessit%C3%A0)" title="BQP (complessità)">BQP</a><b>&#160;·</b> <a href="/wiki/BPP_(complessit%C3%A0)" title="BPP (complessità)">BPP</a><b>&#160;·</b> <a href="/wiki/RP_(complessit%C3%A0)" title="RP (complessità)">RP</a><b>&#160;·</b> <a href="/wiki/ZPP_(complessit%C3%A0)" title="ZPP (complessità)">ZPP</a><b>&#160;·</b> <a href="/w/index.php?title=PCP_(complessit%C3%A0)&amp;action=edit&amp;redlink=1" class="new" title="PCP (complessità) (la pagina non esiste)">PCP</a><b>&#160;·</b> <a href="/w/index.php?title=IP_(complessit%C3%A0)&amp;action=edit&amp;redlink=1" class="new" title="IP (complessità) (la pagina non esiste)">IP</a><b>&#160;·</b> <a href="/w/index.php?title=PH_(complessit%C3%A0)&amp;action=edit&amp;redlink=1" class="new" title="PH (complessità) (la pagina non esiste)">PH</a></td></tr></tbody></table> <div class="noprint" style="width:100%; 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