{"product_id":"bounded-arithmetic-propositional-logic-and-complexity-theory-hardback-9780521452052","title":"Bounded Arithmetic, Propositional Logic and Complexity Theory (Hardback) 9780521452052","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eBounded Arithmetic, Propositional Logic and Complexity Theory\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cem\u003eDiscusses the deep connections between logic and complexity theory, and lists a number of intriguing open problems.\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eJan Krajicek (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9780521452052, Cambridge University Press\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 24 November 1995\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e360 pages\u003cbr\u003e24.2 x 16.2 x 2.7 cm, 0.65 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'It can be strongly recommended especially to mathematicians and computer scientists working in the field and to graduate students.' European Mathematical Society Newsletter\u003c\/font\u003e\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eThis book presents an up-to-date, unified treatment of research in bounded arithmetic and complexity of propositional logic, with emphasis on independence proofs and lower bound proofs. The author discusses the deep connections between logic and complexity theory and lists a number of intriguing open problems. An introduction to the basics of logic and complexity theory is followed by discussion of important results in propositional proof systems and systems of bounded arithmetic. More advanced topics are then treated, including polynomial simulations and conservativity results, various witnessing theorems, the translation of bounded formulas (and their proofs) into propositional ones, the method of random partial restrictions and its applications, direct independence proofs, complete systems of partial relations, lower bounds to the size of constant-depth propositional proofs, the method of Boolean valuations, the issue of hard tautologies and optimal proof systems, combinatorics and complexity theory within bounded arithmetic, and relations to complexity issues of predicate calculus. Students and researchers in mathematical logic and complexity theory will find this comprehensive treatment an excellent guide to this expanding interdisciplinary area.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e1. Introduction\u003cbr\u003e 2. Preliminaries\u003cbr\u003e 3. Basic complexity theory\u003cbr\u003e 4. Basic propositional logic\u003cbr\u003e 5. Basic bounded arithmetic\u003cbr\u003e 6. Definability of computations\u003cbr\u003e 7. Witnessing theorems\u003cbr\u003e 8. Definability and witnessing in second order theories\u003cbr\u003e 9. Translations of arithmetic formulas\u003cbr\u003e 10. Finite axiomatizability problem\u003cbr\u003e 11. Direct independence proofs\u003cbr\u003e 12. Bounds for constant-depth Frege systems\u003cbr\u003e 13. Bounds for Frege and extended Frege systems\u003cbr\u003e 14. Hard tautologies and optimal proof systems\u003cbr\u003e 15. Strength of bounded arithmetic\u003cbr\u003e References\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], Mathematical foundations [\u003ca title=\"See our other books on Mathematical foundations\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematical%20foundations%20%5BPBC%5D%22\"\u003ePBC\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":46005689778456,"sku":"9780521452052","price":122.89,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/products\/9780521452052i_06cc1d14-9a57-4fd1-a648-4a1a430bf4cf.jpg?v=1691382232","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/bounded-arithmetic-propositional-logic-and-complexity-theory-hardback-9780521452052","provider":"Freshly Printed Books","version":"1.0","type":"link"}