{"product_id":"formal-languages-automata-and-numeration-systems-2-applications-to-recognizability-and-decidability-hardback-9781848217881","title":"Formal Languages, Automata and Numeration Systems 2; Applications to Recognizability and Decidability (Hardback) 9781848217881","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eFormal Languages, Automata and Numeration Systems 2\u003c\/font\u003e\u003cbr\u003e\r\n\u003cfont size=\"5\"\u003eApplications to Recognizability and Decidability\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eMichel Rigo (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9781848217881, Wiley\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 4 November 2014\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e272 pages\u003cbr\u003e23.6 x 15.8 x 2 cm, 0.567 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cem\u003e\u003cfont size=\"3\"\u003e\"This book follows \u003ci\u003eFormal Languages, Automata and Numeration Systems. Vol. 1. Introduction to Combinatorics on Words\u003c\/i\u003e. It contains essentially two parts that are quite interesting.\" (\u003ci\u003eZentralblatt MATH\u003c\/i\u003e 2016)\u003c\/font\u003e\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003e\u003cp\u003e\u003cb\u003eThe interplay between words, computability, algebra and arithmetic has now proved its relevance and fruitfulness. Indeed, the cross-fertilization between formal logic and finite automata (such as that initiated by J.R. Büchi) or between combinatorics on words and number theory has paved the way to recent dramatic developments, for example, the transcendence results for the real numbers having a \"simple\" binary expansion, by B. Adamczewski and Y. Bugeaud.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eThis book is at the heart of this interplay through a unified exposition. Objects are considered with a perspective that comes both from theoretical computer science and mathematics. Theoretical computer science offers here topics such as decision problems and recognizability issues, whereas mathematics offers concepts such as discrete dynamical systems.\u003c\/p\u003e \u003cp\u003eThe main goal is to give a quick access, for students and researchers in mathematics or computer science, to actual research topics at the intersection between automata and formal language theory, number theory and combinatorics on words.\u003c\/p\u003e \u003cp\u003eThe second of two volumes on this subject, this book covers regular languages, numeration systems, formal methods applied to decidability issues about infinite words and sets of numbers.\u003c\/p\u003e\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e\u003cp\u003eForeword ix\u003c\/p\u003e \u003cp\u003eIntroduction XIII\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 1. Crash Course On Regular Languages 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Automata and regular languages 2\u003c\/p\u003e \u003cp\u003e1.2 Adjacency matrix 14\u003c\/p\u003e \u003cp\u003e1.3 Multidimensional alphabet 17\u003c\/p\u003e \u003cp\u003e1.4 Two pumping lemmas 19\u003c\/p\u003e \u003cp\u003e1.5 The minimal automaton 23\u003c\/p\u003e \u003cp\u003e1.6 Some operations preserving regularity 29\u003c\/p\u003e \u003cp\u003e1.7 Links with automatic sequences and recognizable sets 32\u003c\/p\u003e \u003cp\u003e1.8 Polynomial regular languages 37\u003c\/p\u003e \u003cp\u003e1.8.1 Tiered words 40\u003c\/p\u003e \u003cp\u003e1.8.2 Characterization of regular languages of polynomial growth 43\u003c\/p\u003e \u003cp\u003e1.8.3 Growing letters in morphic words 49\u003c\/p\u003e \u003cp\u003e1.9 Bibliographic notes and comments 51\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 2. A Range Of Numeration Systems 55\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Substitutive systems 58\u003c\/p\u003e \u003cp\u003e2.2 Abstract numeration systems 67\u003c\/p\u003e \u003cp\u003e2.2.1 Generalization of Cobham’s theorem on automatic sequences 74\u003c\/p\u003e \u003cp\u003e2.2.2 Some properties of abstract numeration systems 86\u003c\/p\u003e \u003cp\u003e2.3 Positional numeration systems 89\u003c\/p\u003e \u003cp\u003e2.4 Pisot numeration systems 98\u003c\/p\u003e \u003cp\u003e2.5 Back to β-expansions 107\u003c\/p\u003e \u003cp\u003e2.5.1 Representation of real numbers 107\u003c\/p\u003e \u003cp\u003e2.5.2 Link between representations of integers and real numbers 112\u003c\/p\u003e \u003cp\u003e2.5.3 Ito–Sadahiro negative base systems 114\u003c\/p\u003e \u003cp\u003e2.6 Miscellaneous systems 117\u003c\/p\u003e \u003cp\u003e2.7 Bibliographical notes and comments 123\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 3. Logical Framework and Decidability Issues 129\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 A glimpse at mathematical logic 132\u003c\/p\u003e \u003cp\u003e3.1.1 Syntax 132\u003c\/p\u003e \u003cp\u003e3.1.2 Semantics 136\u003c\/p\u003e \u003cp\u003e3.2 Decision problems and decidability 140\u003c\/p\u003e \u003cp\u003e3.3 Quantifier elimination in Presburger arithmetic 143\u003c\/p\u003e \u003cp\u003e3.3.1 Equivalent structures 143\u003c\/p\u003e \u003cp\u003e3.3.2 Presburger’s theorem and quantifier elimination 146\u003c\/p\u003e \u003cp\u003e3.3.3 Some consequences of Presburger’s theorem 150\u003c\/p\u003e \u003cp\u003e3.4 Büchi’s theorem 156\u003c\/p\u003e \u003cp\u003e3.4.1 Definable sets 157\u003c\/p\u003e \u003cp\u003e3.4.2 A constructive proof of Büchi’s theorem 159\u003c\/p\u003e \u003cp\u003e3.4.3 Extension to Pisot numeration systems 168\u003c\/p\u003e \u003cp\u003e3.5 Some applications 170\u003c\/p\u003e \u003cp\u003e3.5.1 Properties about automatic sequences 170\u003c\/p\u003e \u003cp\u003e3.5.2 Overlap-freeness 172\u003c\/p\u003e \u003cp\u003e3.5.3 Abelian unbordered factors 173\u003c\/p\u003e \u003cp\u003e3.5.4 Periodicity 177\u003c\/p\u003e \u003cp\u003e3.5.5 Factors 178\u003c\/p\u003e \u003cp\u003e3.5.6 Applications to Pisot numeration systems 180\u003c\/p\u003e \u003cp\u003e3.6 Bibliographic notes and comments 183\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 4 List Of Sequences 187\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eBibliography 193\u003c\/p\u003e \u003cp\u003eIndex 231\u003c\/p\u003e \u003cp\u003eSummary of Volume 1 235\u003c\/p\u003e\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Electronics \u0026amp; communications engineering [\u003ca title=\"See our other books on Electronics \u0026amp; communications engineering\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Electronics%20\u0026amp;%20communications%20engineering%20%5BTJ%5D%22\"\u003eTJ\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Wiley-ISTE","offers":[{"title":"Brand New","offer_id":52449392230680,"sku":"9781848217881","price":100.57,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/files\/9781848217881.jpg?v=1785197882","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/formal-languages-automata-and-numeration-systems-2-applications-to-recognizability-and-decidability-hardback-9781848217881","provider":"Freshly Printed Books","version":"1.0","type":"link"}