A Combinatorial Approach to Collapsing Words
Given a word w over a finite alphabet Σ and a finite deterministic automaton \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{docu...
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| creator | Cherubini, A. Gawrychowski, P. Kisielewicz, A. Piochi, B. |
| description | Given a word w over a finite alphabet Σ and a finite deterministic automaton \documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}${\mathcal A} = {\langle} Q,\Sigma,\delta {\rangle}$\end{document}, the inequality |δ(Q,w)| ≤|Q|–n means that under the natural action of the word w the image of the state set Q is reduced by at least n states. The word w is n-collapsing if this inequality holds for any deterministic finite automaton that satisfies such an inequality for at least one word. In this paper we present a new approach to the topic of collapsing words, and announce a few results we have obtained using this new approach. In particular, we present a direct proof of the fact that the language of n-collapsing words is recursive. |
| doi_str_mv | 10.1007/11821069_23 |
| format | Book Chapter |
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\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
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\begin{document}${\mathcal A} = {\langle} Q,\Sigma,\delta {\rangle}$\end{document}, the inequality |δ(Q,w)| ≤|Q|–n means that under the natural action of the word w the image of the state set Q is reduced by at least n states. The word w is n-collapsing if this inequality holds for any deterministic finite automaton that satisfies such an inequality for at least one word. In this paper we present a new approach to the topic of collapsing words, and announce a few results we have obtained using this new approach. In particular, we present a direct proof of the fact that the language of n-collapsing words is recursive.</description><identifier>ISSN: 0302-9743</identifier><identifier>ISBN: 3540377913</identifier><identifier>ISBN: 9783540377917</identifier><identifier>EISSN: 1611-3349</identifier><identifier>EISBN: 354037793X</identifier><identifier>EISBN: 9783540377931</identifier><identifier>DOI: 10.1007/11821069_23</identifier><language>eng</language><publisher>Berlin, Heidelberg: Springer Berlin Heidelberg</publisher><subject>Applied sciences ; Computer science; control theory; systems ; Exact sciences and technology ; Theoretical computing</subject><ispartof>Lecture notes in computer science, 2006, p.256-266</ispartof><rights>Springer-Verlag Berlin Heidelberg 2006</rights><rights>2008 INIST-CNRS</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><relation>Lecture Notes in Computer Science</relation></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/11821069_23$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/11821069_23$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>309,310,775,776,780,785,786,789,4036,4037,27902,38232,41418,42487</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=19938198$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><contributor>Urzyczyn, Paweł</contributor><contributor>Královič, Rastislav</contributor><creatorcontrib>Cherubini, A.</creatorcontrib><creatorcontrib>Gawrychowski, P.</creatorcontrib><creatorcontrib>Kisielewicz, A.</creatorcontrib><creatorcontrib>Piochi, B.</creatorcontrib><title>A Combinatorial Approach to Collapsing Words</title><title>Lecture notes in computer science</title><description>Given a word w over a finite alphabet Σ and a finite deterministic automaton \documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
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\usepackage{upgreek}
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\begin{document}${\mathcal A} = {\langle} Q,\Sigma,\delta {\rangle}$\end{document}, the inequality |δ(Q,w)| ≤|Q|–n means that under the natural action of the word w the image of the state set Q is reduced by at least n states. The word w is n-collapsing if this inequality holds for any deterministic finite automaton that satisfies such an inequality for at least one word. In this paper we present a new approach to the topic of collapsing words, and announce a few results we have obtained using this new approach. In particular, we present a direct proof of the fact that the language of n-collapsing words is recursive.</description><subject>Applied sciences</subject><subject>Computer science; control theory; systems</subject><subject>Exact sciences and technology</subject><subject>Theoretical computing</subject><issn>0302-9743</issn><issn>1611-3349</issn><isbn>3540377913</isbn><isbn>9783540377917</isbn><isbn>354037793X</isbn><isbn>9783540377931</isbn><fulltext>true</fulltext><rsrctype>book_chapter</rsrctype><creationdate>2006</creationdate><recordtype>book_chapter</recordtype><recordid>eNpNkEtLxEAQhMcXuBs9-Qdy8SAY7Z5OMpnjEnzBghdFb0NPNrNGs5kwsxf__UZW0ENRUF_RDSXEBcINAqhbxEoilNpIOhBzKnIgpTS9H4oZlogZUa6P_gDSsZgBgcy0yulUzGP8BACptJyJ60Va-43tBt760HGfLsYxeG4-0q2fSN_zGLthnb75sIpn4sRxH9vzX0_E6_3dS_2YLZ8fnurFMhtlUW4zXZFFsA6KyrUFK8eoyimyFotcaXCNta6EBnLlCoeEjBIrNUnKFTJRIi73d0eODfcu8NB00Yyh23D4Nqg1VTh9ScTVvhcnNKzbYKz3X9EgmJ-hzL-haAdcYlPT</recordid><startdate>2006</startdate><enddate>2006</enddate><creator>Cherubini, A.</creator><creator>Gawrychowski, P.</creator><creator>Kisielewicz, A.</creator><creator>Piochi, B.</creator><general>Springer Berlin Heidelberg</general><general>Springer</general><scope>IQODW</scope></search><sort><creationdate>2006</creationdate><title>A Combinatorial Approach to Collapsing Words</title><author>Cherubini, A. ; Gawrychowski, P. ; Kisielewicz, A. ; Piochi, B.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-p256t-983b10bf058fe5a7fa1763b1bb154790fcbbf60c047f5f131a1218721822d1a33</frbrgroupid><rsrctype>book_chapters</rsrctype><prefilter>book_chapters</prefilter><language>eng</language><creationdate>2006</creationdate><topic>Applied sciences</topic><topic>Computer science; control theory; systems</topic><topic>Exact sciences and technology</topic><topic>Theoretical computing</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Cherubini, A.</creatorcontrib><creatorcontrib>Gawrychowski, P.</creatorcontrib><creatorcontrib>Kisielewicz, A.</creatorcontrib><creatorcontrib>Piochi, B.</creatorcontrib><collection>Pascal-Francis</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Cherubini, A.</au><au>Gawrychowski, P.</au><au>Kisielewicz, A.</au><au>Piochi, B.</au><au>Urzyczyn, Paweł</au><au>Královič, Rastislav</au><format>book</format><genre>bookitem</genre><ristype>CHAP</ristype><atitle>A Combinatorial Approach to Collapsing Words</atitle><btitle>Lecture notes in computer science</btitle><seriestitle>Lecture Notes in Computer Science</seriestitle><date>2006</date><risdate>2006</risdate><spage>256</spage><epage>266</epage><pages>256-266</pages><issn>0302-9743</issn><eissn>1611-3349</eissn><isbn>3540377913</isbn><isbn>9783540377917</isbn><eisbn>354037793X</eisbn><eisbn>9783540377931</eisbn><abstract>Given a word w over a finite alphabet Σ and a finite deterministic automaton \documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}${\mathcal A} = {\langle} Q,\Sigma,\delta {\rangle}$\end{document}, the inequality |δ(Q,w)| ≤|Q|–n means that under the natural action of the word w the image of the state set Q is reduced by at least n states. The word w is n-collapsing if this inequality holds for any deterministic finite automaton that satisfies such an inequality for at least one word. In this paper we present a new approach to the topic of collapsing words, and announce a few results we have obtained using this new approach. In particular, we present a direct proof of the fact that the language of n-collapsing words is recursive.</abstract><cop>Berlin, Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.1007/11821069_23</doi><tpages>11</tpages><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0302-9743 |
| ispartof | Lecture notes in computer science, 2006, p.256-266 |
| issn | 0302-9743 1611-3349 |
| language | eng |
| recordid | cdi_pascalfrancis_primary_19938198 |
| source | Springer Books |
| subjects | Applied sciences Computer science control theory systems Exact sciences and technology Theoretical computing |
| title | A Combinatorial Approach to Collapsing Words |
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