{"product_id":"automatic-sequences-theory-applications-generalizations-hardback-9780521823326","title":"Automatic Sequences; Theory, Applications, Generalizations (Hardback) 9780521823326","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eAutomatic Sequences\u003c\/font\u003e\u003cbr\u003e\r\n\u003cfont size=\"5\"\u003eTheory, Applications, Generalizations\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cem\u003eThis book is the first integrated treatment of sequences generated by finite automata and their generalizations.\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eJean-Paul Allouche (Author), Jeffrey Shallit (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9780521823326, Cambridge University Press\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 21 July 2003\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e588 pages, 170 b\/w illus.  548 exercises\u003cbr\u003e26.6 x 17.9 x 3.8 cm, 1.157 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'Allouche and Shallit's books presents an introduction to the fascinating subject of automatic sequences. This is the first book that systematically develops the theory of these sequences.' Zentralblatt MATH\u003c\/font\u003e\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eUniting dozens of seemingly disparate results from different fields, this book combines concepts from mathematics and computer science to present the first integrated treatment of sequences generated by 'finite automata'. The authors apply the theory to the study of automatic sequences and their generalizations, such as Sturmian words and k-regular sequences. And further, they provide applications to number theory (particularly to formal power series and transcendence in finite characteristic), physics, computer graphics, and music. Starting from first principles wherever feasible, basic results from combinatorics on words, numeration systems, and models of computation are discussed. Thus this book is suitable for graduate students or advanced undergraduates, as well as for mature researchers wishing to know more about this fascinating subject. Results are presented from first principles wherever feasible, and the book is supplemented by a collection of 460 exercises, 85 open problems, and over 1600 citations to the literature.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePreface\u003cbr\u003e 1. Stringology\u003cbr\u003e 2. Number theory and algebra\u003cbr\u003e 3. Numeration systems\u003cbr\u003e 4. Finite automata and other models of computation\u003cbr\u003e 5. Automatic sequences\u003cbr\u003e 6. Uniform morphisms and automatic sequences\u003cbr\u003e 7. Morphic sequences\u003cbr\u003e 8. Frequency of letters\u003cbr\u003e 9. Characteristic words\u003cbr\u003e 10. Subwords\u003cbr\u003e 11. Cobham's theorem\u003cbr\u003e 12. Formal power series\u003cbr\u003e 13. Automatic real numbers\u003cbr\u003e 14. Multidimensional automatic sequences\u003cbr\u003e 15. Automaticity\u003cbr\u003e 16. k-regular sequences\u003cbr\u003e 17. Physics\u003cbr\u003e Appendix. Hints, references and solutions for selected exercises\u003cbr\u003e Bibliography\u003cbr\u003e Index.\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Mathematical theory of computation [\u003ca title=\"See our other books on Mathematical theory of computation\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematical%20theory%20of%20computation%20%5BUYA%5D%22\"\u003eUYA\u003c\/a\u003e], Number theory [\u003ca title=\"See our other books on Number theory\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Number%20theory%20%5BPBH%5D%22\"\u003ePBH\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":46004363428120,"sku":"9780521823326","price":73.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/products\/9780521823326i_a52c96bc-d6ca-46e6-9ee6-43720675af3a.jpg?v=1691368412","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/automatic-sequences-theory-applications-generalizations-hardback-9780521823326","provider":"Freshly Printed Books","version":"1.0","type":"link"}