CiNii 図書 - Rudiments of μ-calculus

<!DOCTYPE html> <html lang="ja" itemscope itemtype="http://schema.org/Book"> <head> <script type="text/javascript" src="/books/js/preview.js?V171012"></script> <script type="text/javascript" src="/books/js/elinklist_disclosure.js?V141104"></script> <meta http-equiv="content-type" content="text/html; charset=utf-8" /> <meta http-equiv="X-UA-Compatible" content="IE=edge,chrome=1" /> <meta http-equiv="content-style-type" content="text/css" /> <meta http-equiv="content-script-type" content="text/javascript" /> <meta name="viewport" content="width=device-width,user-scalable=no" /> <meta name="format-detection" content="telephone=no"> <link rel="stylesheet" type="text/css" href="/books/style/slick.css?V190423"> <link rel="stylesheet" type="text/css" href="/books/style/slick-theme.css?V190423"> <link rel="stylesheet" type="text/css" href="/books/style/slick-ext.css?V190423"> <link rel="shortcut icon" href="/books/images/favicon.ico" type="image/vnd.microsoft.icon" /> <link href="/books/style/cinii.css?V202209" rel="stylesheet" type="text/css" /> <script type="text/javascript" src="/books/js/jquery-3.7.1.min.js"></script> <script type="text/javascript" src="/books/js/bootstrap.min.js"></script> <script type="text/javascript" src="/books/js/cinii.js?V151027"></script> <script type="text/javascript" src="/books/js/html5shiv-printshiv.min.js"></script> <script type="text/javascript" src="/books/js/respond.min.js"></script> <script type="text/javascript" src="/books/js/common.js?V240716"></script> <script type="text/javascript" src="/books/js/changeDisplayMode.js?V190913"></script> <script type="text/javascript" src="/books/js/transferParameterCir.js?240724"></script> <script async src="https://www.googletagmanager.com/gtag/js?id=G-5YXF8KWH9K"></script> <link rel="search" type="application/opensearchdescription+xml" title="CiNii Books" href="/books/opensearch/description.xml" /> <link rel="search" type="application/opensearchdescription+xml" title="CiNii Books - Exact title match" href="/books/opensearch/exact-title.xml" /> <link rel="search" type="application/opensearchdescription+xml" title="CiNii Books - Author Search" href="/books/opensearch/author.xml" />  <title>CiNii 図書 - Rudiments of μ-calculus</title> <link rel="meta" type="application/rdf+xml" title="RDF" href="/ncid/BA50939760.rdf" /> <link rel="meta" type="application/json" title="JSON-LD 1.0" href="/ncid/BA50939760.json" /> <link rel="canonical" href="https://ci.nii.ac.jp/ncid/BA50939760" /> <link rel="amphtml" href="https://ci.nii.ac.jp/ncid/BA50939760.amp" /> <meta name="dc.title" content="Rudiments of μ-calculus" /> <meta name="dc.creator" content="Arnold, André" /> <meta name="dc.creator" content="Niwiński, Damian" /> <meta name="dc.publisher" content="Elsevier" /> <meta name="dc.date" content="2001" /> <meta name="dc.type" content="book" /> <meta name="citation_abstract_html_url" content="https://ci.nii.ac.jp/ncid/BA50939760" /> <meta property="og:title" content="CiNii 図書 - Rudiments of μ-calculus" /> <meta property="og:description" content="Rudiments of μ-calculus A. Arnold, D. Niwiński （Studies in logic and the foundations of mathematics, v. 146） Elsevier, 2001" /> <meta property="og:type" content="book" /> <meta property="og:url" content="https://ci.nii.ac.jp/ncid/BA50939760" /> <meta property="og:site_name" content="CiNii Books" /> <meta property="fb:admins" content="701886930" /> <meta name="twitter:card" content="summary" /> <meta name="twitter:site" content="@cinii_jp" /> <meta itemprop="name" content="CiNii 図書 - Rudiments of μ-calculus" /> <script type="application/ld+json"> { "@context": "http://schema.org", "@type": "Article", "name": "Rudiments of μ-calculus", "author": { "@type": "Person", "name": "A. Arnold, D. Niwiński" }, "publisher": { "@type":"Organization", "name": "Elsevier" }, "datePublished": "2001", "description": "Bibliography: p. [269]-273\nIncludes index\n1.Complete lattices and fixed-point theorems\n2. The mu-calculi: Syntax and semantics\n3.The Boolean mu-calculus\n4.Parity Games\n5.The mu-calculus on words\n6.The mucalculus over powerset algebras\n7.The mu-calculus versus automata\n8.Hierachy problems\n9.Distributivity and normal form results\n10.Decision problems\n11.Algorithms\nThis book presents what in our opinion constitutes the basis of the theory of the mu-calculus, considered as an algebraic system rather than a logic. We have wished to present the subject in a unified way, and in a form as general as possible. Therefore, our emphasis is on the generality of the fixed-point notation, and on the connections between mu-calculus, games, and automata, which we also explain in an algebraic way.\n\n This book should be accessible for graduate or advanced undergraduate students both in mathematics and computer science. We have designed this book especially for researchers and students interested in logic in computer science, comuter aided verification, and general aspects of automata theory. We have aimed at gathering in a single place the fundamental results of the theory, that are currently very scattered in the literature, and often hardly accessible for interested readers.\n\n The presentation is self-contained, except for the proof of the Mc-Naughton's Determinization Theorem (see, e.g., [97]. However, we suppose that the reader is already familiar with some basic automata theory and universal algebra. The references, credits, and suggestions for further reading are given at the end of each chapter.\n", "url": "https://ci.nii.ac.jp/ncid/BA50939760", "headline": "Rudiments of μ-calculus" } </script></head> <body class="books detail with_sidenavi"> <nav class="navbar navbar-header"> <div class="navbar-topcontent"> <a href="/books/" id="system_ci_jp" class="navbar-brand headerlogo">CiNii 国立情報学研究所学術情報ナビゲータ[サイニィ]</a>  <button type="button" class="navbar-toggle button-menu collapsed" data-toggle="collapse" data-target="#nav-content"> メニュー </button> <button type="button" class="navbar-toggle button-search collapsed" data-toggle="collapse" data-target="#searchbox"> 検索 </button> </div> <div id="nav-content" class="collapse navbar-collapse headermenu"> <ul class="nav navbar-nav menu-service-list"> <li><a href="https://cir.nii.ac.jp/" onclick="return transferParameterCir(this, 'https://cir.nii.ac.jp', true, 'cir');" class="menu-service-item"><div>論文・データをさがす</div></a></li> <li class="active"><a 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src="/books/js/utils.js?V190913"></script> <script type="text/javascript"> window.initSearchBox('book', false); </script> <div class="servicestop_information"><div id="servicestop_information"> <ul><li><a href="https://support.nii.ac.jp/ja/cir/cib_integration">【2023年10月31日掲載】CiNii BooksのCiNii Researchへの統合について</a></li> <li><a href="https://support.nii.ac.jp/ja/news/cinii/20250227">英国Nielsen Book Services社提供データの削除について</a></li> <li><a href="https://support.nii.ac.jp/ja/news/cinii/20250318">CiNiiのサービスに関するアンケートを実施中です（期間：2025年3月18日(火)から2025年4月17日(木)まで）</a></li> </ul> </div> </div> <div class="container-hasSubnav"> <div class="maincontents"> <div id="itemdatatext" class="itemdatatext"> <div class="itemheading paperdata"> <h1 class="book_class entry-title"> <span>Rudiments of μ-calculus</span> </h1> <div id="authors" class="authorsContainer hidden-xs"> <ul> <li class="authorslist"> <div class="authordata author vcard"> <ul> <li class="authorname"> <a href="/author/DA04270776"> <span class="authorname fn">Arnold, André</span> </a> </li> </ul> </div> </li> <li class="authorslist"> <div class="authordata author vcard"> <ul> <li class="authorname"> <span class="authorname fn">Niwiński, Damian</span> </li> </ul> </div> </li> </ul> </div> <div id="numofrelateditem"> <ul> <li class="referencelink"><a href="#ref">関連文献: 1件</a></li> </ul> </div> </div> <div class="sectionofdata visible-xs"> <h2 class="heading">著者</h2> <div class="authorsContainer"> <ul class="row"> <li class="authorslist"> <div class="authordata author vcard"> <ul> <li class="authorname"> <a href="/author/DA04270776"> <span class="fn">Arnold, André</span> </a> </li> </ul> </div> </li> <li class="authorslist"> <div class="authordata author vcard"> <ul> <li class="authorname"> <span class="fn">Niwiński, Damian</span> </li> </ul> </div> </li> </ul> </div> </div> <div class="sectionofdata"> <h2 class="heading">書誌事項</h2> <div class="dataContainer bibliographicdata"> <p class="bblp-title trd">Rudiments of μ-calculus</p> <p class="bblp-author al">A. Arnold, D. Niwiński</p> <p class="bblp-series ptbtr-ptbno">（Studies in logic and the foundations of mathematics, v. 146）</p> <p class="bblp-publish publ-pubdt">Elsevier, 2001</p> <ul class="bblp-vols vlsr clearfix"> </ul> <p class="bblp-type gmd"></p> </div> </div> <div class="sectionofdata" id="anc-library-top"> <div class="listheading"> <h2 class="heading" id="anc-library">大学図書館所蔵&emsp;<span class="library-fulfillNum"><span id="pNummatches"><span id="numFiltered"></span>件 / </span>全<span class="numoflibrary">29</span>件</span></h2> <script type="text/javascript"> //<![CDATA[ var libraryFilteringSource = "<div class=\"library-filtering clearfix\">" + "<p>" + "<select id=\"kcFilter\" class=\"filter-kencode\" onchange=\"onFilterChanged()\">" + "<option filter=\"kc\" selected=\"selected\" value=\"null\">すべての地域</option>" + "<option filter=\"kc\" value=\"01\" class=\"ken\">北海道</option>" + "<option filter=\"kc\" value=\"02 03 04 05 06 07 \" class=\"region\">東北地方</option>" + "<option filter=\"kc\" 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url('/books/images/exbanner-calil.gif') left no-repeat;"><a target="_blank" href="https://calil.jp/book/0444506209" onclick="gtag('event', 'click', {'event_category': 'access', 'event_action': 'click', 'event_label': 'Search-Calil'});">カーリル</a></li> <li class="externallinkL worldcat" style="background:transparent url('/books/images/exbanner-worldcat.png') left no-repeat;"><a target="_blank" href="https://search.worldcat.org/search?q=bn:0444506209" onclick="gtag('event', 'click', {'event_category': 'access', 'event_action': 'click', 'event_label': 'Search-WorldCat'});">WorldCat</a></li> </ul> </div> </div> <div class="sectionofdata"> <h2 class="heading">注記</h2> <div class="dataContainer biblio-note nt"> <p>Bibliography: p. [269]-273</p> <p>Includes index</p> </div> </div> <div class="sectionofdata"> <h2 class="headingbar">内容説明・目次</h2> <div class="dataContainer biblio-contents toc"> <p class="toc-kind">内容説明</p> <div class="toc-body">This book presents what in our opinion constitutes the basis of the theory of the mu-calculus, considered as an algebraic system rather than a logic. We have wished to present the subject in a unified way, and in a form as general as possible. Therefore, our emphasis is on the generality of the fixed-point notation, and on the connections between mu-calculus, games, and automata, which we also explain in an algebraic way. This book should be accessible for graduate or advanced undergraduate students both in mathematics and computer science. We have designed this book especially for researchers and students interested in logic in computer science, comuter aided verification, and general aspects of automata theory. We have aimed at gathering in a single place the fundamental results of the theory, that are currently very scattered in the literature, and often hardly accessible for interested readers. The presentation is self-contained, except for the proof of the Mc-Naughton's Determinization Theorem (see, e.g., [97]. However, we suppose that the reader is already familiar with some basic automata theory and universal algebra. The references, credits, and suggestions for further reading are given at the end of each chapter.</div> <p class="toc-kind">目次</p> <div class="toc-body">1.Complete lattices and fixed-point theorems 2. The mu-calculi: Syntax and semantics 3.The Boolean mu-calculus 4.Parity Games 5.The mu-calculus on words 6.The mucalculus over powerset algebras 7.The mu-calculus versus automata 8.Hierachy problems 9.Distributivity and normal form results 10.Decision problems 11.Algorithms</div> <p class="toc-provided-by"> 「Nielsen BookData」より</p> </div> </div> <div class="sectionofdata"> <div class="listheading"> <h2 id="ref" class="heading">関連文献：&ensp;1件中 &ensp;1-1を表示</h2> </div> <div class="listContainer related-article_list"> <ul> <li class="oddline"> <div class="listitem xfolkentry"> <div class="list_number hidden-xs">1</div> <dl class="book_class"> <dt class="item_mainTitle item_title trd"> <a href="/ncid/BA00099329" class="taggedlink">Studies in logic and the foundations of mathematics</a> </dt> <dd> <p class="item_subData item_authordata"></p> <p class="item_data item_publishdata"> <span class="pblc">North-Holland</span> </p> <p class="item_data item_bibotherdata"> </p> </dd> </dl> </div> 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CiNii 図書 - Rudiments of μ-calculus