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클레이니 스타 - 위키백과, 우리 모두의 백과사전
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0.5em;width:100%;font-size:small}.mw-parser-output .ambox .mbox-image{border:none;padding:2px 0 2px 0.5em;text-align:center}.mw-parser-output .ambox .mbox-imageright{border:none;padding:2px 0.5em 2px 0;text-align:center}.mw-parser-output .ambox .mbox-empty-cell{border:none;padding:0;width:1px}.mw-parser-output .ambox .mbox-image-div{width:52px}html.client-js body.skin-minerva .mw-parser-output .mbox-text-span{margin-left:23px!important}@media(min-width:720px){.mw-parser-output .ambox{margin:0 10%}}</style> <table class="plainlinks metadata ambox ambox-content" role="presentation"> <tbody> <tr> <td class="mbox-text"> <div class="mbox-text-span"> 이 문서의 내용은 <b><a href="https://ko-m-wikipedia-org.translate.goog/wiki/%EC%9C%84%ED%82%A4%EB%B0%B1%EA%B3%BC:%EC%B6%9C%EC%B2%98_%EB%B0%9D%ED%9E%88%EA%B8%B0?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="위키백과:출처 밝히기">출처</a>가 분명하지 않습니다.</b><span class="hide-when-compact"><br> 이 <span class="plainlinks"><a class="external text" 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class="date">2013년 2월</span></small>)</span> </div></td> </tr> </tbody> </table> <p><b>클레이니 스타</b>(Kleene Star)는 <a href="https://ko-m-wikipedia-org.translate.goog/wiki/%EB%AC%B8%EC%9E%90%EC%97%B4?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="문자열">문자열</a>이나 <a href="https://ko-m-wikipedia-org.translate.goog/wiki/%EB%AC%B8%EC%9E%90?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="문자">문자</a>의 <a href="https://ko-m-wikipedia-org.translate.goog/wiki/%EC%A7%91%ED%95%A9?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="집합">집합</a>에 쓰이는 <a href="https://ko-m-wikipedia-org.translate.goog/wiki/%EB%8B%A8%ED%95%AD_%EC%97%B0%EC%82%B0?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="mw-redirect" title="단항 연산">단항 연산</a>으로, 0개 이상의 임의 원소의 <a href="https://ko-m-wikipedia-org.translate.goog/w/index.php?title=%EC%97%B0%EC%87%84&action=edit&redlink=1&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="new" title="연쇄 (없는 문서)">연쇄</a>를 뜻한다. <a href="https://ko-m-wikipedia-org.translate.goog/wiki/%EC%8A%A4%ED%8B%B0%EB%B8%90_%ED%81%B4%EB%A0%88%EC%9D%B4%EB%8B%88?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="스티븐 클레이니">스티븐 클레이니</a>가 도입하였으며, <a href="https://ko-m-wikipedia-org.translate.goog/wiki/%EC%98%A4%ED%86%A0%EB%A7%88%ED%83%80_%EC%9D%B4%EB%A1%A0?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="오토마타 이론">오토마타 이론</a>과 <a href="https://ko-m-wikipedia-org.translate.goog/wiki/%EC%A0%95%EA%B7%9C_%ED%91%9C%ED%98%84%EC%8B%9D?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="정규 표현식">정규 표현식</a>, <a href="https://ko-m-wikipedia-org.translate.goog/wiki/%ED%98%95%EC%8B%9D_%EB%AC%B8%EB%B2%95?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="형식 문법">형식 문법</a>에서 활용된다. 일반적으로 수학에서는 자유 <a href="https://ko-m-wikipedia-org.translate.goog/wiki/%EB%AA%A8%EB%85%B8%EC%9D%B4%EB%93%9C?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="모노이드">모노이드</a> 구성에 쓰인다. <b>Σ*</b>는 시그마의 클레이너 스타, 또는 간단히 시그마 스타라고 읽는다.</p> <div id="toc" class="toc" role="navigation" aria-labelledby="mw-toc-heading"> <input type="checkbox" role="button" id="toctogglecheckbox" class="toctogglecheckbox" style="display:none"> <div class="toctitle" lang="ko" dir="ltr"> <h2 id="mw-toc-heading">목차</h2><span class="toctogglespan"><label class="toctogglelabel" for="toctogglecheckbox"></label></span> </div> <ul> <li class="toclevel-1 tocsection-1"><a href="https://ko-m-wikipedia-org.translate.goog/wiki/%ED%81%B4%EB%A0%88%EC%9D%B4%EB%8B%88_%EC%8A%A4%ED%83%80?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#%EC%A0%95%EC%9D%98"><span class="tocnumber">1</span> <span class="toctext">정의</span></a> <ul> <li class="toclevel-2 tocsection-2"><a href="https://ko-m-wikipedia-org.translate.goog/wiki/%ED%81%B4%EB%A0%88%EC%9D%B4%EB%8B%88_%EC%8A%A4%ED%83%80?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#%ED%81%B4%EB%A0%88%EC%9D%B4%EB%8B%88_%ED%94%8C%EB%9F%AC%EC%8A%A4"><span class="tocnumber">1.1</span> <span class="toctext">클레이니 플러스</span></a></li> </ul></li> <li class="toclevel-1 tocsection-3"><a href="https://ko-m-wikipedia-org.translate.goog/wiki/%ED%81%B4%EB%A0%88%EC%9D%B4%EB%8B%88_%EC%8A%A4%ED%83%80?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#%EC%98%88%EC%8B%9C"><span class="tocnumber">2</span> <span class="toctext">예시</span></a> <ul> <li class="toclevel-2 tocsection-4"><a href="https://ko-m-wikipedia-org.translate.goog/wiki/%ED%81%B4%EB%A0%88%EC%9D%B4%EB%8B%88_%EC%8A%A4%ED%83%80?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#%EB%AA%A8%EB%85%B8%EC%9D%B4%EB%93%9C_%EA%B5%AC%EC%84%B1"><span class="tocnumber">2.1</span> <span class="toctext">모노이드 구성</span></a></li> </ul></li> <li class="toclevel-1 tocsection-5"><a href="https://ko-m-wikipedia-org.translate.goog/wiki/%ED%81%B4%EB%A0%88%EC%9D%B4%EB%8B%88_%EC%8A%A4%ED%83%80?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#%EA%B0%99%EC%9D%B4_%EB%B3%B4%EA%B8%B0"><span class="tocnumber">3</span> <span class="toctext">같이 보기</span></a></li> </ul> </div> </section> <div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(1)"> <span class="indicator mf-icon mf-icon-expand mf-icon--small"></span> <h2 id="정의"><span id=".EC.A0.95.EC.9D.98"></span>정의</h2><span class="mw-editsection"> <a role="button" href="https://ko-m-wikipedia-org.translate.goog/w/index.php?title=%ED%81%B4%EB%A0%88%EC%9D%B4%EB%8B%88_%EC%8A%A4%ED%83%80&action=edit&section=1&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="부분 편집: 정의" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> <span class="minerva-icon minerva-icon--edit"></span> <span>편집</span> </a> </span> </div> <section class="mf-section-1 collapsible-block" id="mf-section-1"> <p>집합 V의 임의 n회 연쇄를 다음과 같이 정의한다.</p> <dl> <dd> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V^{0}=\{\varepsilon \}}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi> V </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 0 </mn> </mrow> </msup> <mo> = </mo> <mo fence="false" stretchy="false"> { </mo> <mi> ε<!-- ε --> </mi> <mo fence="false" stretchy="false"> } </mo> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle V^{0}=\{\varepsilon \}} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/04a156ce4f06dcc59cca336992705b0469377a4b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.478ex; height:3.176ex;" alt="{\displaystyle V^{0}=\{\varepsilon \}}"> </noscript><span class="lazy-image-placeholder" style="width: 9.478ex;height: 3.176ex;vertical-align: -0.838ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/04a156ce4f06dcc59cca336992705b0469377a4b" data-alt="{\displaystyle V^{0}=\{\varepsilon \}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> </dd> <dd> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V^{1}=V}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi> V </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 1 </mn> </mrow> </msup> <mo> = </mo> <mi> V </mi> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle V^{1}=V} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6d476fd9b82610e89cb524060974f3ab22c1fd14" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.857ex; height:2.676ex;" alt="{\displaystyle V^{1}=V}"> </noscript><span class="lazy-image-placeholder" style="width: 7.857ex;height: 2.676ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6d476fd9b82610e89cb524060974f3ab22c1fd14" data-alt="{\displaystyle V^{1}=V}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> </dd> <dd> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V^{n}=V\circ V^{n-1}=\{uv|u\in V,v\in V^{n-1}\}(n\geq 2)}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi> V </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> n </mi> </mrow> </msup> <mo> = </mo> <mi> V </mi> <mo> ∘<!-- ∘ --> </mo> <msup> <mi> V </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> n </mi> <mo> −<!-- − --> </mo> <mn> 1 </mn> </mrow> </msup> <mo> = </mo> <mo fence="false" stretchy="false"> { </mo> <mi> u </mi> <mi> v </mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false"> | </mo> </mrow> <mi> u </mi> <mo> ∈<!-- ∈ --> </mo> <mi> V </mi> <mo> , </mo> <mi> v </mi> <mo> ∈<!-- ∈ --> </mo> <msup> <mi> V </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> n </mi> <mo> −<!-- − --> </mo> <mn> 1 </mn> </mrow> </msup> <mo fence="false" stretchy="false"> } </mo> <mo stretchy="false"> ( </mo> <mi> n </mi> <mo> ≥<!-- ≥ --> </mo> <mn> 2 </mn> <mo stretchy="false"> ) </mo> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle V^{n}=V\circ V^{n-1}=\{uv|u\in V,v\in V^{n-1}\}(n\geq 2)} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b2493bec53c5748d0e90c922aa40f6d37d6e32d2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:47.64ex; height:3.176ex;" alt="{\displaystyle V^{n}=V\circ V^{n-1}=\{uv|u\in V,v\in V^{n-1}\}(n\geq 2)}"> </noscript><span class="lazy-image-placeholder" style="width: 47.64ex;height: 3.176ex;vertical-align: -0.838ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b2493bec53c5748d0e90c922aa40f6d37d6e32d2" data-alt="{\displaystyle V^{n}=V\circ V^{n-1}=\{uv|u\in V,v\in V^{n-1}\}(n\geq 2)}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> </dd> </dl> <p>이 때 V의 클레이니 스타는 다음과 같이 정의한다.</p> <dl> <dd> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V^{*}=\sideset {}{_{i=0}^{\infty }}\bigcup V^{i}=\bigcup _{i\in \mathbb {N} }V^{i}=\{\varepsilon \}\cup V\cup V^{2}\cup V^{3}\cup V^{4}\cup \ldots .}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi> V </mi> <mrow class="MJX-TeXAtom-ORD"> <mo> ∗<!-- ∗ --> </mo> </mrow> </msup> <mo> = </mo> <mrow class="MJX-TeXAtom-OP"> <mrow class="MJX-TeXAtom-OP MJX-fixedlimits"> <mrow class="MJX-TeXAtom-ORD"> <mpadded width="0"> <mrow class="MJX-TeXAtom-ORD"> <mphantom> <mo> ⋃<!-- ⋃ --> </mo> </mphantom> </mrow> </mpadded> </mrow> </mrow> <mspace width="negativethinmathspace"></mspace> <msubsup> <mrow class="MJX-TeXAtom-OP MJX-fixedlimits"> <mo movablelimits="false"> ⋃<!-- ⋃ --> </mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal"> ∞<!-- ∞ --> </mi> </mrow> </msubsup> </mrow> <mo> <!-- --> </mo> <msup> <mi> V </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> </msup> <mo> = </mo> <munder> <mo> ⋃<!-- ⋃ --> </mo> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> <mo> ∈<!-- ∈ --> </mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck"> N </mi> </mrow> </mrow> </munder> <msup> <mi> V </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> </msup> <mo> = </mo> <mo fence="false" stretchy="false"> { </mo> <mi> ε<!-- ε --> </mi> <mo fence="false" stretchy="false"> } </mo> <mo> ∪<!-- ∪ --> </mo> <mi> V </mi> <mo> ∪<!-- ∪ --> </mo> <msup> <mi> V </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msup> <mo> ∪<!-- ∪ --> </mo> <msup> <mi> V </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 3 </mn> </mrow> </msup> <mo> ∪<!-- ∪ --> </mo> <msup> <mi> V </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 4 </mn> </mrow> </msup> <mo> ∪<!-- ∪ --> </mo> <mo> …<!-- … --> </mo> <mo> . </mo> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle V^{*}=\sideset {}{_{i=0}^{\infty }}\bigcup V^{i}=\bigcup _{i\in \mathbb {N} }V^{i}=\{\varepsilon \}\cup V\cup V^{2}\cup V^{3}\cup V^{4}\cup \ldots .} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/487f5024c6f33cf234bda8c3de72156de863f860" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:57.585ex; height:5.676ex;" alt="{\displaystyle V^{*}=\sideset {}{_{i=0}^{\infty }}\bigcup V^{i}=\bigcup _{i\in \mathbb {N} }V^{i}=\{\varepsilon \}\cup V\cup V^{2}\cup V^{3}\cup V^{4}\cup \ldots .}"> </noscript><span class="lazy-image-placeholder" style="width: 57.585ex;height: 5.676ex;vertical-align: -3.171ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/487f5024c6f33cf234bda8c3de72156de863f860" data-alt="{\displaystyle V^{*}=\sideset {}{_{i=0}^{\infty }}\bigcup V^{i}=\bigcup _{i\in \mathbb {N} }V^{i}=\{\varepsilon \}\cup V\cup V^{2}\cup V^{3}\cup V^{4}\cup \ldots .}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> </dd> </dl> <div class="mw-heading mw-heading3"> <h3 id="클레이니_플러스"><span id=".ED.81.B4.EB.A0.88.EC.9D.B4.EB.8B.88_.ED.94.8C.EB.9F.AC.EC.8A.A4"></span>클레이니 플러스</h3><span class="mw-editsection"> <a role="button" href="https://ko-m-wikipedia-org.translate.goog/w/index.php?title=%ED%81%B4%EB%A0%88%EC%9D%B4%EB%8B%88_%EC%8A%A4%ED%83%80&action=edit&section=2&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="부분 편집: 클레이니 플러스" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> <span class="minerva-icon minerva-icon--edit"></span> <span>편집</span> </a> </span> </div> <p>클레이니 플러스는 다음과 같이 정의된다.빈 문자열을 포함하지 않는 클레이니 스타이다.</p> <dl> <dd> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V^{+}=\sideset {}{_{i=1}^{\infty }}\bigcup V^{i}=V\cup V^{2}\cup V^{3}\cup V^{4}\cup \ldots .=VV^{*}}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi> V </mi> <mrow class="MJX-TeXAtom-ORD"> <mo> + </mo> </mrow> </msup> <mo> = </mo> <mrow class="MJX-TeXAtom-OP"> <mrow class="MJX-TeXAtom-OP MJX-fixedlimits"> <mrow class="MJX-TeXAtom-ORD"> <mpadded width="0"> <mrow class="MJX-TeXAtom-ORD"> <mphantom> <mo> ⋃<!-- ⋃ --> </mo> </mphantom> </mrow> </mpadded> </mrow> </mrow> <mspace width="negativethinmathspace"></mspace> <msubsup> <mrow class="MJX-TeXAtom-OP MJX-fixedlimits"> <mo movablelimits="false"> ⋃<!-- ⋃ --> </mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal"> ∞<!-- ∞ --> </mi> </mrow> </msubsup> </mrow> <mo> <!-- --> </mo> <msup> <mi> V </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> </msup> <mo> = </mo> <mi> V </mi> <mo> ∪<!-- ∪ --> </mo> <msup> <mi> V </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msup> <mo> ∪<!-- ∪ --> </mo> <msup> <mi> V </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 3 </mn> </mrow> </msup> <mo> ∪<!-- ∪ --> </mo> <msup> <mi> V </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 4 </mn> </mrow> </msup> <mo> ∪<!-- ∪ --> </mo> <mo> …<!-- … --> </mo> <mo> . </mo> <mo> = </mo> <mi> V </mi> <msup> <mi> V </mi> <mrow class="MJX-TeXAtom-ORD"> <mo> ∗<!-- ∗ --> </mo> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle V^{+}=\sideset {}{_{i=1}^{\infty }}\bigcup V^{i}=V\cup V^{2}\cup V^{3}\cup V^{4}\cup \ldots .=VV^{*}} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2d8f8cc65a89a69dc04de27776ebe62a629f1846" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.338ex; width:50.597ex; height:3.843ex;" alt="{\displaystyle V^{+}=\sideset {}{_{i=1}^{\infty }}\bigcup V^{i}=V\cup V^{2}\cup V^{3}\cup V^{4}\cup \ldots .=VV^{*}}"> </noscript><span class="lazy-image-placeholder" style="width: 50.597ex;height: 3.843ex;vertical-align: -1.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2d8f8cc65a89a69dc04de27776ebe62a629f1846" data-alt="{\displaystyle V^{+}=\sideset {}{_{i=1}^{\infty }}\bigcup V^{i}=V\cup V^{2}\cup V^{3}\cup V^{4}\cup \ldots .=VV^{*}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> </dd> </dl> <p>여기서 <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 V}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> V </mi> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle V} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/af0f6064540e84211d0ffe4dac72098adfa52845" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.787ex; height:2.176ex;" alt="{\displaystyle V}"> </noscript><span class="lazy-image-placeholder" style="width: 1.787ex;height: 2.176ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/af0f6064540e84211d0ffe4dac72098adfa52845" data-alt="{\displaystyle V}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span>가 빈 문자열을 포함하지 않는다면 클레이니 플러스는 빈 문자열을 포함하지 않는 클레이니 스타와 같다.</p> <dl> <dd> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V^{+}=V^{*}-\{\varepsilon \}}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi> V </mi> <mrow class="MJX-TeXAtom-ORD"> <mo> + </mo> </mrow> </msup> <mo> = </mo> <msup> <mi> V </mi> <mrow class="MJX-TeXAtom-ORD"> <mo> ∗<!-- ∗ --> </mo> </mrow> </msup> <mo> −<!-- − --> </mo> <mo fence="false" stretchy="false"> { </mo> <mi> ε<!-- ε --> </mi> <mo fence="false" stretchy="false"> } </mo> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle V^{+}=V^{*}-\{\varepsilon \}} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/65c4383b7162e09d45cbbee70f200006a9d7be92" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:15.746ex; height:3.009ex;" alt="{\displaystyle V^{+}=V^{*}-\{\varepsilon \}}"> </noscript><span class="lazy-image-placeholder" style="width: 15.746ex;height: 3.009ex;vertical-align: -0.838ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/65c4383b7162e09d45cbbee70f200006a9d7be92" data-alt="{\displaystyle V^{+}=V^{*}-\{\varepsilon \}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> </dd> </dl> <p><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 V}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> V </mi> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle V} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/af0f6064540e84211d0ffe4dac72098adfa52845" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.787ex; height:2.176ex;" alt="{\displaystyle V}"> </noscript><span class="lazy-image-placeholder" style="width: 1.787ex;height: 2.176ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/af0f6064540e84211d0ffe4dac72098adfa52845" data-alt="{\displaystyle V}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span>가 빈 문자열을 포함한다면 클레이니 플러스는 클레이니 스타와 같다.</p> <dl> <dd> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V^{+}=V^{*}}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi> V </mi> <mrow class="MJX-TeXAtom-ORD"> <mo> + </mo> </mrow> </msup> <mo> = </mo> <msup> <mi> V </mi> <mrow class="MJX-TeXAtom-ORD"> <mo> ∗<!-- ∗ --> </mo> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle V^{+}=V^{*}} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9fa1f40ea4c6244eb2f057cce99677d3e3c0b9d9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:9.497ex; height:2.509ex;" alt="{\displaystyle V^{+}=V^{*}}"> </noscript><span class="lazy-image-placeholder" style="width: 9.497ex;height: 2.509ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9fa1f40ea4c6244eb2f057cce99677d3e3c0b9d9" data-alt="{\displaystyle V^{+}=V^{*}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> </dd> </dl> </section> <div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(2)"> <span class="indicator mf-icon mf-icon-expand mf-icon--small"></span> <h2 id="예시"><span id=".EC.98.88.EC.8B.9C"></span>예시</h2><span class="mw-editsection"> <a role="button" href="https://ko-m-wikipedia-org.translate.goog/w/index.php?title=%ED%81%B4%EB%A0%88%EC%9D%B4%EB%8B%88_%EC%8A%A4%ED%83%80&action=edit&section=3&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="부분 편집: 예시" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> <span class="minerva-icon minerva-icon--edit"></span> <span>편집</span> </a> </span> </div> <section class="mf-section-2 collapsible-block" id="mf-section-2"> <ul> <li>{a, b}* = {</li> </ul> <dl> <dd> <dl> <dd> ε, </dd> <dd> a, b, </dd> <dd> aa, ab, ba, bb, </dd> <dd> aaa, aab, aba, abb, baa, bab, bba, bbb, </dd> </dl> </dd> <dd> ...} </dd> </dl> <ul> <li>{ab, c}* = {</li> </ul> <dl> <dd> <dl> <dd> ε, </dd> <dd> ab, c, </dd> <dd> abab, abc, cab, cc, </dd> <dd> ababab, ababc, abcab, abcc, cabab, cabc, ccab, ccc, </dd> </dl> </dd> <dd> ...} </dd> </dl> <ul> <li><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 \varnothing ^{*}=\{\varepsilon \}}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi class="MJX-variant"> ∅<!-- ∅ --> </mi> <mrow class="MJX-TeXAtom-ORD"> <mo> ∗<!-- ∗ --> </mo> </mrow> </msup> <mo> = </mo> <mo fence="false" stretchy="false"> { </mo> <mi> ε<!-- ε --> </mi> <mo fence="false" stretchy="false"> } </mo> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \varnothing ^{*}=\{\varepsilon \}} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6d27c42f8da5fb9d13e2618deb1e76529bc1e291" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.369ex; height:2.843ex;" alt="{\displaystyle \varnothing ^{*}=\{\varepsilon \}}"> </noscript><span class="lazy-image-placeholder" style="width: 9.369ex;height: 2.843ex;vertical-align: -0.838ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6d27c42f8da5fb9d13e2618deb1e76529bc1e291" data-alt="{\displaystyle \varnothing ^{*}=\{\varepsilon \}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span></li> <li><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 \varnothing ^{+}=\varnothing \varnothing ^{*}=\{\}=\varnothing }"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi class="MJX-variant"> ∅<!-- ∅ --> </mi> <mrow class="MJX-TeXAtom-ORD"> <mo> + </mo> </mrow> </msup> <mo> = </mo> <mi class="MJX-variant"> ∅<!-- ∅ --> </mi> <msup> <mi class="MJX-variant"> ∅<!-- ∅ --> </mi> <mrow class="MJX-TeXAtom-ORD"> <mo> ∗<!-- ∗ --> </mo> </mrow> </msup> <mo> = </mo> <mo fence="false" stretchy="false"> { </mo> <mo fence="false" stretchy="false"> } </mo> <mo> = </mo> <mi class="MJX-variant"> ∅<!-- ∅ --> </mi> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \varnothing ^{+}=\varnothing \varnothing ^{*}=\{\}=\varnothing } </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2cf936af7dd8e18627aab6cc29a61b609e97dfd8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:21.418ex; height:3.009ex;" alt="{\displaystyle \varnothing ^{+}=\varnothing \varnothing ^{*}=\{\}=\varnothing }"> </noscript><span class="lazy-image-placeholder" style="width: 21.418ex;height: 3.009ex;vertical-align: -0.838ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2cf936af7dd8e18627aab6cc29a61b609e97dfd8" data-alt="{\displaystyle \varnothing ^{+}=\varnothing \varnothing ^{*}=\{\}=\varnothing }" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span></li> </ul> <div class="mw-heading mw-heading3"> <h3 id="모노이드_구성"><span id=".EB.AA.A8.EB.85.B8.EC.9D.B4.EB.93.9C_.EA.B5.AC.EC.84.B1"></span>모노이드 구성</h3><span class="mw-editsection"> <a role="button" href="https://ko-m-wikipedia-org.translate.goog/w/index.php?title=%ED%81%B4%EB%A0%88%EC%9D%B4%EB%8B%88_%EC%8A%A4%ED%83%80&action=edit&section=4&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="부분 편집: 모노이드 구성" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> <span class="minerva-icon minerva-icon--edit"></span> <span>편집</span> </a> </span> </div> <p><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 (M,\cdot )}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false"> ( </mo> <mi> M </mi> <mo> , </mo> <mo> ⋅<!-- ⋅ --> </mo> <mo stretchy="false"> ) </mo> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle (M,\cdot )} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8dc86a0f0f83580455b11737df738e30a314e49a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.932ex; height:2.843ex;" alt="{\displaystyle (M,\cdot )}"> </noscript><span class="lazy-image-placeholder" style="width: 5.932ex;height: 2.843ex;vertical-align: -0.838ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8dc86a0f0f83580455b11737df738e30a314e49a" data-alt="{\displaystyle (M,\cdot )}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span>이 모노이드라 가정하자. 연쇄 연산은 결합법칙을 만족하므로, 즉 ε∈M이고 M은 연쇄 연산에 닫혀 있다. 이 때 M의 부분집합 N에 대해 N을 포함하는 최소의 모노이드는 <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^{*},\cdot )}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false"> ( </mo> <msup> <mi> N </mi> <mrow class="MJX-TeXAtom-ORD"> <mo> ∗<!-- ∗ --> </mo> </mrow> </msup> <mo> , </mo> <mo> ⋅<!-- ⋅ --> </mo> <mo stretchy="false"> ) </mo> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle (N^{*},\cdot )} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d47e75bde4aac439be3014cb514b060a3dcf8e04" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.667ex; height:2.843ex;" alt="{\displaystyle (N^{*},\cdot )}"> </noscript><span class="lazy-image-placeholder" style="width: 6.667ex;height: 2.843ex;vertical-align: -0.838ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d47e75bde4aac439be3014cb514b060a3dcf8e04" data-alt="{\displaystyle (N^{*},\cdot )}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span>이다.</p> </section> <div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(3)"> <span class="indicator mf-icon mf-icon-expand mf-icon--small"></span> <h2 id="같이_보기"><span id=".EA.B0.99.EC.9D.B4_.EB.B3.B4.EA.B8.B0"></span>같이 보기</h2><span class="mw-editsection"> <a role="button" href="https://ko-m-wikipedia-org.translate.goog/w/index.php?title=%ED%81%B4%EB%A0%88%EC%9D%B4%EB%8B%88_%EC%8A%A4%ED%83%80&action=edit&section=5&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="부분 편집: 같이 보기" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> <span class="minerva-icon minerva-icon--edit"></span> <span>편집</span> </a> </span> </div> <section class="mf-section-3 collapsible-block" id="mf-section-3"> <ul> <li><a href="https://ko-m-wikipedia-org.translate.goog/wiki/%EC%A0%95%EA%B7%9C_%EC%96%B8%EC%96%B4?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="정규 언어">정규 언어</a></li> <li><a href="https://ko-m-wikipedia-org.translate.goog/wiki/%EC%A0%95%EA%B7%9C_%ED%91%9C%ED%98%84%EC%8B%9D?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="정규 표현식">정규 표현식</a></li> </ul> <div class="navbox-styles"> <style data-mw-deduplicate="TemplateStyles:r36480591">.mw-parser-output .hlist dl,.mw-parser-output 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Rendering was triggered because: page-view --> </section> </div><!-- MobileFormatter took 0.007 seconds --><!--esi <esi:include src="/esitest-fa8a495983347898/content" /> --> <noscript> <img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?useformat=mobile&type=1x1&usesul3=0" alt="" width="1" height="1" style="border: none; position: absolute;"> </noscript> <div class="printfooter" data-nosnippet=""> 원본 주소 "<a dir="ltr" href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://ko.wikipedia.org/w/index.php?title%3D%ED%81%B4%EB%A0%88%EC%9D%B4%EB%8B%88_%EC%8A%A4%ED%83%80%26oldid%3D31910385">https://ko.wikipedia.org/w/index.php?title=클레이니_스타&oldid=31910385</a>" </div> </div> </div> <div class="post-content" id="page-secondary-actions"> </div> </main> <footer class="mw-footer minerva-footer" role="contentinfo"><a class="last-modified-bar" href="https://ko-m-wikipedia-org.translate.goog/w/index.php?title=%ED%81%B4%EB%A0%88%EC%9D%B4%EB%8B%88_%EC%8A%A4%ED%83%80&action=history&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB"> <div class="post-content last-modified-bar__content"><span class="minerva-icon minerva-icon-size-medium minerva-icon--modified-history"></span> <span class="last-modified-bar__text modified-enhancement" data-user-name="A.TedBot" data-user-gender="unknown" data-timestamp="1645894470"> <span>2022년 2월 27일 (일) 01:54에 마지막으로 편집됨</span> </span> <span class="minerva-icon minerva-icon-size-small minerva-icon--expand"></span> </div></a> <div class="post-content footer-content"> <div id="mw-data-after-content"> <div class="read-more-container"></div> </div> <div id="p-lang"> <h4>언어</h4> <section> <ul id="p-variants" class="minerva-languages"></ul> <ul class="minerva-languages"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://ar.wikipedia.org/wiki/%25D9%2586%25D8%25AC%25D9%2585%25D8%25A9_%25D9%2583%25D9%2584%25D9%258A%25D9%2586" title="نجمة كلين – 아랍어" lang="ar" hreflang="ar" data-title="نجمة كلين" data-language-autonym="العربية" data-language-local-name="아랍어" class="interlanguage-link-target"><span>العربية</span></a></li> <li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://bs.wikipedia.org/wiki/Kleeneov_operator" title="Kleeneov operator – 보스니아어" lang="bs" hreflang="bs" data-title="Kleeneov operator" data-language-autonym="Bosanski" data-language-local-name="보스니아어" class="interlanguage-link-target"><span>Bosanski</span></a></li> <li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://ca.wikipedia.org/wiki/Clausura_de_Kleene" title="Clausura de Kleene – 카탈로니아어" lang="ca" hreflang="ca" data-title="Clausura de Kleene" data-language-autonym="Català" data-language-local-name="카탈로니아어" class="interlanguage-link-target"><span>Català</span></a></li> <li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://cs.wikipedia.org/wiki/Kleeneho_hv%25C4%259Bzdi%25C4%258Dka" title="Kleeneho hvězdička – 체코어" lang="cs" hreflang="cs" data-title="Kleeneho hvězdička" data-language-autonym="Čeština" data-language-local-name="체코어" class="interlanguage-link-target"><span>Čeština</span></a></li> <li class="interlanguage-link interwiki-de mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://de.wikipedia.org/wiki/Kleenesche_und_positive_H%25C3%25BClle" title="Kleenesche und positive Hülle – 독일어" lang="de" hreflang="de" data-title="Kleenesche und positive Hülle" data-language-autonym="Deutsch" data-language-local-name="독일어" class="interlanguage-link-target"><span>Deutsch</span></a></li> <li class="interlanguage-link interwiki-el mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://el.wikipedia.org/wiki/%25CE%2591%25CF%2583%25CF%2584%25CE%25AD%25CF%2581%25CE%25B9_%25CE%259A%25CE%25BB%25CE%25AD%25CE%25B9%25CE%25BD%25CE%25B9" title="Αστέρι Κλέινι – 그리스어" lang="el" hreflang="el" data-title="Αστέρι Κλέινι" data-language-autonym="Ελληνικά" data-language-local-name="그리스어" class="interlanguage-link-target"><span>Ελληνικά</span></a></li> <li class="interlanguage-link interwiki-en mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://en.wikipedia.org/wiki/Kleene_star" title="Kleene star – 영어" lang="en" hreflang="en" data-title="Kleene star" data-language-autonym="English" data-language-local-name="영어" class="interlanguage-link-target"><span>English</span></a></li> <li class="interlanguage-link interwiki-es mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://es.wikipedia.org/wiki/Clausura_de_Kleene" title="Clausura de Kleene – 스페인어" lang="es" hreflang="es" data-title="Clausura de Kleene" data-language-autonym="Español" data-language-local-name="스페인어" class="interlanguage-link-target"><span>Español</span></a></li> <li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://eu.wikipedia.org/wiki/Kleene_izar" title="Kleene izar – 바스크어" lang="eu" hreflang="eu" data-title="Kleene izar" data-language-autonym="Euskara" data-language-local-name="바스크어" class="interlanguage-link-target"><span>Euskara</span></a></li> <li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://fa.wikipedia.org/wiki/%25D8%25B3%25D8%25AA%25D8%25A7%25D8%25B1%25D9%2587_%25DA%25A9%25D9%2584%25DB%258C%25D9%2586" title="ستاره کلین – 페르시아어" lang="fa" hreflang="fa" data-title="ستاره کلین" data-language-autonym="فارسی" data-language-local-name="페르시아어" class="interlanguage-link-target"><span>فارسی</span></a></li> <li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://fi.wikipedia.org/wiki/Kleenen_t%25C3%25A4hti" title="Kleenen tähti – 핀란드어" lang="fi" hreflang="fi" data-title="Kleenen tähti" data-language-autonym="Suomi" data-language-local-name="핀란드어" class="interlanguage-link-target"><span>Suomi</span></a></li> <li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://fr.wikipedia.org/wiki/%25C3%2589toile_de_Kleene" title="Étoile de Kleene – 프랑스어" lang="fr" hreflang="fr" data-title="Étoile de Kleene" data-language-autonym="Français" data-language-local-name="프랑스어" class="interlanguage-link-target"><span>Français</span></a></li> <li class="interlanguage-link interwiki-he mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://he.wikipedia.org/wiki/%25D7%259B%25D7%2595%25D7%259B%25D7%2591_%25D7%25A7%25D7%259C%25D7%2599%25D7%259F" title="כוכב קלין – 히브리어" lang="he" hreflang="he" data-title="כוכב קלין" data-language-autonym="עברית" data-language-local-name="히브리어" class="interlanguage-link-target"><span>עברית</span></a></li> <li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://hr.wikipedia.org/wiki/Kleeneov_operator" title="Kleeneov operator – 크로아티아어" lang="hr" hreflang="hr" data-title="Kleeneov operator" data-language-autonym="Hrvatski" data-language-local-name="크로아티아어" class="interlanguage-link-target"><span>Hrvatski</span></a></li> <li class="interlanguage-link interwiki-it mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://it.wikipedia.org/wiki/Star_di_Kleene" title="Star di Kleene – 이탈리아어" lang="it" hreflang="it" data-title="Star di Kleene" data-language-autonym="Italiano" data-language-local-name="이탈리아어" class="interlanguage-link-target"><span>Italiano</span></a></li> <li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://ja.wikipedia.org/wiki/%25E3%2582%25AF%25E3%2583%25AA%25E3%2583%25BC%25E3%2583%258D%25E9%2596%2589%25E5%258C%2585" title="クリーネ閉包 – 일본어" lang="ja" hreflang="ja" data-title="クリーネ閉包" data-language-autonym="日本語" data-language-local-name="일본어" class="interlanguage-link-target"><span>日本語</span></a></li> <li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://ms.wikipedia.org/wiki/Bintang_Kleene" title="Bintang Kleene – 말레이어" lang="ms" hreflang="ms" data-title="Bintang Kleene" data-language-autonym="Bahasa Melayu" data-language-local-name="말레이어" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li> <li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://nl.wikipedia.org/wiki/Kleene-ster" title="Kleene-ster – 네덜란드어" lang="nl" hreflang="nl" data-title="Kleene-ster" data-language-autonym="Nederlands" data-language-local-name="네덜란드어" class="interlanguage-link-target"><span>Nederlands</span></a></li> <li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://nn.wikipedia.org/wiki/Kleenestjerne" title="Kleenestjerne – 노르웨이어(니노르스크)" lang="nn" hreflang="nn" data-title="Kleenestjerne" data-language-autonym="Norsk nynorsk" data-language-local-name="노르웨이어(니노르스크)" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li> <li class="interlanguage-link interwiki-no mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://no.wikipedia.org/wiki/Kleenestjerne" title="Kleenestjerne – 노르웨이어(보크말)" lang="nb" hreflang="nb" data-title="Kleenestjerne" data-language-autonym="Norsk bokmål" data-language-local-name="노르웨이어(보크말)" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li> <li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://pl.wikipedia.org/wiki/Domkni%25C4%2599cie_Kleene%25E2%2580%2599ego" title="Domknięcie Kleene’ego – 폴란드어" lang="pl" hreflang="pl" data-title="Domknięcie Kleene’ego" data-language-autonym="Polski" data-language-local-name="폴란드어" class="interlanguage-link-target"><span>Polski</span></a></li> <li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://pt.wikipedia.org/wiki/Fecho_de_Kleene" title="Fecho de Kleene – 포르투갈어" lang="pt" hreflang="pt" data-title="Fecho de Kleene" data-language-autonym="Português" data-language-local-name="포르투갈어" class="interlanguage-link-target"><span>Português</span></a></li> <li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://ro.wikipedia.org/wiki/%25C3%258Enchidere_Kleene" title="Închidere Kleene – 루마니아어" lang="ro" hreflang="ro" data-title="Închidere Kleene" data-language-autonym="Română" data-language-local-name="루마니아어" class="interlanguage-link-target"><span>Română</span></a></li> <li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://ru.wikipedia.org/wiki/%25D0%2597%25D0%25B2%25D0%25B5%25D0%25B7%25D0%25B4%25D0%25B0_%25D0%259A%25D0%25BB%25D0%25B8%25D0%25BD%25D0%25B8" title="Звезда Клини – 러시아어" lang="ru" hreflang="ru" data-title="Звезда Клини" data-language-autonym="Русский" data-language-local-name="러시아어" class="interlanguage-link-target"><span>Русский</span></a></li> <li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://simple.wikipedia.org/wiki/Kleene_star" title="Kleene star – Simple English" lang="en-simple" hreflang="en-simple" data-title="Kleene star" 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://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://sr.wikipedia.org/wiki/%25D0%259A%25D0%25BB%25D0%25B8%25D0%25BD%25D0%25B8%25D1%2598%25D0%25B5%25D0%25B2%25D0%25BE_%25D0%25B7%25D0%25B0%25D1%2582%25D0%25B2%25D0%25BE%25D1%2580%25D0%25B5%25D1%259A%25D0%25B5" title="Клинијево затворење – 세르비아어" lang="sr" hreflang="sr" data-title="Клинијево затворење" data-language-autonym="Српски / srpski" data-language-local-name="세르비아어" class="interlanguage-link-target"><span>Српски / srpski</span></a></li> <li class="interlanguage-link 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