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Available in 24 languages" > <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 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%82%D8%B3%D9%85_%D8%AA%D8%B9%D9%82%D9%8A%D8%AF" title="قسم تعقيد – Arabic" lang="ar" hreflang="ar" data-title="قسم تعقيد" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Classe_de_complexitat" title="Classe de complexitat – Catalan" lang="ca" hreflang="ca" data-title="Classe de complexitat" data-language-autonym="Català" data-language-local-name="Catalan" 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 – German" lang="de" hreflang="de" data-title="Komplexitätsklasse" data-language-autonym="Deutsch" data-language-local-name="German" 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 – English" lang="en" hreflang="en" data-title="Complexity class" data-language-autonym="English" data-language-local-name="English" 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 – Spanish" lang="es" hreflang="es" data-title="Clase de complejidad" data-language-autonym="Español" data-language-local-name="Spanish" 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 – Persian" lang="fa" hreflang="fa" data-title="کلاس پیچیدگی" data-language-autonym="فارسی" data-language-local-name="Persian" 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 – French" lang="fr" hreflang="fr" data-title="Classe de complexité" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</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 – Korean" lang="ko" hreflang="ko" data-title="복잡도 종류" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</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 – Croatian" lang="hr" hreflang="hr" data-title="Klasa složenosti" data-language-autonym="Hrvatski" data-language-local-name="Croatian" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Classe_di_complessit%C3%A0" title="Classe di complessità – Italian" lang="it" hreflang="it" data-title="Classe di complessità" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</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 – Hebrew" lang="he" hreflang="he" data-title="מחלקת סיבוכיות" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Complexiteitsgraad" title="Complexiteitsgraad – Dutch" lang="nl" hreflang="nl" data-title="Complexiteitsgraad" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</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 – 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lang="en" dir="ltr"><p>A <b>Complexity class</b> is a concept from <a href="/wiki/Theoretical_computer_science" title="Theoretical computer science">theoretical computer science</a> and <a href="/wiki/Mathematics" title="Mathematics">mathematics</a>: All problems that have the same <a href="/wiki/Complexity_theory" title="Complexity theory">complexity</a> are in the same complexity class. This means, that for a given input, they need about the same amount of resources, such as compute time, or memory. The most often used models for complexity are <a href="/w/index.php?title=Time_complexity&action=edit&redlink=1" class="new" title="Time complexity (not yet started)">time complexity</a>, which measures the time needed to calculate a result, or space complexity, which looks at the amount of memory or storage needed. When talking about complexity classes, a <i>worst case scenario</i> is usually assumed. </p> <div class="navbox-styles nomobile"><style data-mw-deduplicate="TemplateStyles:r9122492">.mw-parser-output .navbox{box-sizing:border-box;border:1px solid #a2a9b1;width:100%;clear:both;font-size:88%;text-align:center;padding:1px;margin:1em auto 0}.mw-parser-output .navbox .navbox{margin-top:0}.mw-parser-output .navbox+.navbox,.mw-parser-output .navbox+.navbox-styles+.navbox{margin-top:-1px}.mw-parser-output .navbox-inner,.mw-parser-output .navbox-subgroup{width:100%}.mw-parser-output .navbox-group,.mw-parser-output .navbox-title,.mw-parser-output .navbox-abovebelow{padding:0.25em 1em;line-height:1.5em;text-align:center}.mw-parser-output .navbox-group{white-space:nowrap;text-align:right}.mw-parser-output .navbox,.mw-parser-output .navbox-subgroup{background-color:#fdfdfd}.mw-parser-output .navbox-list{line-height:1.5em;border-color:#fdfdfd}.mw-parser-output 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a>span,.mw-parser-output .navbar a>abbr{text-decoration:inherit}.mw-parser-output .navbar-mini abbr{font-variant:small-caps;border-bottom:none;text-decoration:none;cursor:inherit}.mw-parser-output .navbar-ct-full{font-size:114%;margin:0 7em}.mw-parser-output .navbar-ct-mini{font-size:114%;margin:0 4em}</style><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Complexity_classes" title="Template:Complexity classes"><abbr title="View this template" style=";;background:none transparent;border:none;box-shadow:none;padding:0;">v</abbr></a></li><li class="nv-talk"><a href="/w/index.php?title=Template_talk:Complexity_classes&action=edit&redlink=1" class="new" title="Template talk:Complexity classes (not yet started)"><abbr title="Discuss this template" style=";;background:none transparent;border:none;box-shadow:none;padding:0;">t</abbr></a></li><li class="nv-edit"><a class="external text" href="https://simple.wikipedia.org/w/index.php?title=Template:Complexity_classes&action=edit"><abbr title="Edit this template" style=";;background:none transparent;border:none;box-shadow:none;padding:0;">e</abbr></a></li></ul></div><div id="Complexity_classes" style="font-size:114%;margin:0 4em"><a class="mw-selflink selflink">Complexity classes</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Considered feasible</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/w/index.php?title=DLOGTIME&action=edit&redlink=1" class="new" title="DLOGTIME (not yet started)">DLOGTIME</a></li> <li><a href="/w/index.php?title=AC0&action=edit&redlink=1" class="new" title="AC0 (not yet started)">AC<sup>0</sup></a></li> <li><a href="/w/index.php?title=ACC0&action=edit&redlink=1" class="new" title="ACC0 (not yet started)">ACC<sup>0</sup></a></li> <li><a href="/w/index.php?title=TC0&action=edit&redlink=1" class="new" title="TC0 (not yet started)">TC<sup>0</sup></a></li> <li><a href="/w/index.php?title=L_(complexity)&action=edit&redlink=1" class="new" title="L (complexity) (not yet started)">L</a></li> <li><a href="/w/index.php?title=SL_(complexity)&action=edit&redlink=1" class="new" title="SL (complexity) (not yet started)">SL</a></li> <li><a href="/w/index.php?title=RL_(complexity)&action=edit&redlink=1" class="new" title="RL (complexity) (not yet started)">RL</a></li> <li><a href="/w/index.php?title=FL_(complexity)&action=edit&redlink=1" class="new" title="FL (complexity) (not yet started)">FL</a></li> <li><a href="/w/index.php?title=NL_(complexity)&action=edit&redlink=1" class="new" title="NL (complexity) (not yet started)">NL</a> <ul><li><a href="/w/index.php?title=NL-complete&action=edit&redlink=1" class="new" title="NL-complete (not yet started)">NL-complete</a></li></ul></li> <li><a href="/w/index.php?title=NC_(complexity)&action=edit&redlink=1" class="new" title="NC (complexity) (not yet started)">NC</a></li> <li><a href="/w/index.php?title=SC_(complexity)&action=edit&redlink=1" class="new" title="SC (complexity) (not yet started)">SC</a></li> <li><a href="/w/index.php?title=CC_(complexity)&action=edit&redlink=1" class="new" title="CC (complexity) (not yet started)">CC</a></li> <li><a href="/w/index.php?title=P_(complexity)&action=edit&redlink=1" class="new" title="P (complexity) (not yet started)">P</a> <ul><li><a href="/w/index.php?title=P-complete&action=edit&redlink=1" class="new" title="P-complete (not yet started)">P-complete</a></li></ul></li> <li><a href="/w/index.php?title=ZPP_(complexity)&action=edit&redlink=1" class="new" title="ZPP (complexity) (not yet started)">ZPP</a></li> <li><a href="/w/index.php?title=RP_(complexity)&action=edit&redlink=1" class="new" title="RP (complexity) (not yet started)">RP</a></li> <li><a href="/w/index.php?title=BPP_(complexity)&action=edit&redlink=1" class="new" title="BPP (complexity) (not yet started)">BPP</a></li> <li><a href="/w/index.php?title=BQP&action=edit&redlink=1" class="new" title="BQP (not yet started)">BQP</a></li> <li><a href="/w/index.php?title=APX&action=edit&redlink=1" class="new" title="APX (not yet started)">APX</a></li> <li><a href="/w/index.php?title=FP_(complexity)&action=edit&redlink=1" class="new" title="FP (complexity) (not yet started)">FP</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Suspected infeasible</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/w/index.php?title=NP_(complexity)&action=edit&redlink=1" class="new" title="NP (complexity) (not yet started)">NP</a> <ul><li><a href="/wiki/NP-hardness" title="NP-hardness">NP-hard</a></li> <li><a href="/w/index.php?title=NP-completeness&action=edit&redlink=1" class="new" title="NP-completeness (not yet started)">NP-complete</a></li> <li><a href="/w/index.php?title=Co-NP&action=edit&redlink=1" class="new" title="Co-NP (not yet started)">co-NP</a></li> <li><a href="/w/index.php?title=Co-NP-complete&action=edit&redlink=1" class="new" title="Co-NP-complete (not yet started)">co-NP-complete</a></li></ul></li> <li><a href="/w/index.php?title=UP_(complexity)&action=edit&redlink=1" class="new" title="UP (complexity) (not yet started)">UP</a></li> <li><a href="/w/index.php?title=TFNP&action=edit&redlink=1" class="new" title="TFNP (not yet started)">TFNP</a></li> <li><a href="/w/index.php?title=FNP_(complexity)&action=edit&redlink=1" class="new" title="FNP (complexity) (not yet started)">FNP</a></li> <li><a href="/w/index.php?title=Arthur%E2%80%93Merlin_protocol&action=edit&redlink=1" class="new" title="Arthur–Merlin protocol (not yet started)">AM</a></li> <li><a href="/w/index.php?title=QMA&action=edit&redlink=1" class="new" title="QMA (not yet started)">QMA</a></li> <li><a href="/w/index.php?title=PH_(complexity)&action=edit&redlink=1" class="new" title="PH (complexity) (not yet started)">PH</a></li> <li><a href="/w/index.php?title=Parity_P&action=edit&redlink=1" class="new" title="Parity P (not yet started)">⊕P</a></li> <li><a href="/w/index.php?title=PP_(complexity)&action=edit&redlink=1" class="new" title="PP (complexity) (not yet started)">PP</a></li> <li><a href="/w/index.php?title=%E2%99%AFP&action=edit&redlink=1" class="new" title="♯P (not yet started)">#P</a> <ul><li><a href="/w/index.php?title=%E2%99%AFP-complete&action=edit&redlink=1" class="new" title="♯P-complete (not yet started)">#P-complete</a></li></ul></li> <li><a href="/w/index.php?title=IP_(complexity)&action=edit&redlink=1" class="new" title="IP (complexity) (not yet started)">IP</a></li> <li><a href="/w/index.php?title=PSPACE&action=edit&redlink=1" class="new" title="PSPACE (not yet started)">PSPACE</a> <ul><li><a href="/w/index.php?title=PSPACE-complete&action=edit&redlink=1" class="new" title="PSPACE-complete (not yet started)">PSPACE-complete</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Considered infeasible</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/w/index.php?title=EXPTIME&action=edit&redlink=1" class="new" title="EXPTIME (not yet started)">EXPTIME</a></li> <li><a href="/w/index.php?title=NEXPTIME&action=edit&redlink=1" class="new" title="NEXPTIME (not yet started)">NEXPTIME</a></li> <li><a href="/w/index.php?title=EXPSPACE&action=edit&redlink=1" class="new" title="EXPSPACE (not yet started)">EXPSPACE</a></li> <li><a href="/w/index.php?title=2-EXPTIME&action=edit&redlink=1" class="new" title="2-EXPTIME (not yet started)">2-EXPTIME</a></li> <li><a href="/w/index.php?title=ELEMENTARY&action=edit&redlink=1" class="new" title="ELEMENTARY (not yet started)">ELEMENTARY</a></li> <li><a href="/w/index.php?title=PR_(complexity)&action=edit&redlink=1" class="new" title="PR (complexity) (not yet started)">PR</a></li> <li><a href="/w/index.php?title=R_(complexity)&action=edit&redlink=1" class="new" title="R (complexity) (not yet started)">R</a></li> <li><a href="/w/index.php?title=RE_(complexity)&action=edit&redlink=1" class="new" title="RE (complexity) (not yet started)">RE</a></li> <li><a href="/w/index.php?title=ALL_(complexity)&action=edit&redlink=1" class="new" title="ALL (complexity) (not yet started)">ALL</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Class hierarchies</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/w/index.php?title=Polynomial_hierarchy&action=edit&redlink=1" class="new" title="Polynomial hierarchy (not yet started)">Polynomial hierarchy</a></li> <li><a href="/w/index.php?title=Exponential_hierarchy&action=edit&redlink=1" class="new" title="Exponential hierarchy (not yet started)">Exponential hierarchy</a></li> <li><a href="/w/index.php?title=Grzegorczyk_hierarchy&action=edit&redlink=1" class="new" title="Grzegorczyk hierarchy (not yet started)">Grzegorczyk hierarchy</a></li> <li><a href="/w/index.php?title=Arithmetical_hierarchy&action=edit&redlink=1" class="new" title="Arithmetical hierarchy (not yet started)">Arithmetical hierarchy</a></li> <li><a href="/w/index.php?title=Boolean_hierarchy&action=edit&redlink=1" class="new" title="Boolean hierarchy (not yet started)">Boolean hierarchy</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Families of classes</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/w/index.php?title=DTIME&action=edit&redlink=1" class="new" title="DTIME (not yet started)">DTIME</a></li> <li><a href="/w/index.php?title=NTIME&action=edit&redlink=1" class="new" title="NTIME (not yet started)">NTIME</a></li> <li><a href="/w/index.php?title=DSPACE&action=edit&redlink=1" class="new" title="DSPACE (not yet started)">DSPACE</a></li> <li><a href="/w/index.php?title=NSPACE&action=edit&redlink=1" class="new" title="NSPACE (not yet started)">NSPACE</a></li> <li><a href="/w/index.php?title=Probabilistically_checkable_proof&action=edit&redlink=1" class="new" title="Probabilistically checkable proof (not yet started)">Probabilistically checkable proof</a></li> <li><a href="/w/index.php?title=Interactive_proof_system&action=edit&redlink=1" class="new" title="Interactive proof system (not yet started)">Interactive proof system</a></li></ul> </div></td></tr></tbody></table></div> <p><br /> </p> <div class="boilerplate metadata plainlinks" id="stub"><span typeof="mw:File"><a 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