{"product_id":"proof-complexity-generators-paperback-softback-9781009611701","title":"Proof Complexity Generators (Paperback \/ softback) 9781009611701","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eProof Complexity Generators\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cem\u003eDiscover a state-of-the-art theory aiming to construct hard propositional tautologies needed to solve the NP vs. coNP problem.\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eJan Krajíček (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9781009611701, Cambridge University Press\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePaperback \/ softback, published 26 June 2025\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e134 pages\u003cbr\u003e22.8 x 15.2 x 0.8 cm, 0.21 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eThe P vs. NP problem is one of the fundamental problems of mathematics. It asks whether propositional tautologies can be recognized by a polynomial-time algorithm. The problem would be solved in the negative if one could show that there are propositional tautologies that are very hard to prove, no matter how powerful the proof system you use. This is the foundational problem (the NP vs. coNP problem) of proof complexity, an area linking mathematical logic and computational complexity theory. Written by a leading expert in the field, this book presents a theory for constructing such hard tautologies. It introduces the theory step by step, starting with the historic background and a motivational problem in bounded arithmetic, before taking the reader on a tour of various vistas of the field. Finally, it formulates several research problems to highlight new avenues of research.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e1. Introduction\u003cbr\u003e 2. The dWPHP problem\u003cbr\u003e 3. τ-formulas and generators\u003cbr\u003e 4. The stretch\u003cbr\u003e 5. Nisan-Wigderson generator\u003cbr\u003e 6. Gadget generator\u003cbr\u003e 7. The case of ER\u003cbr\u003e 8. Consistency results\u003cbr\u003e 9. Contexts\u003cbr\u003e 10. Further research\u003cbr\u003e Special symbols\u003cbr\u003e References\u003cbr\u003e Index.\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: 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":"Brand New","offer_id":52475076051224,"sku":"9781009611701","price":37.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/files\/9781009611701i.jpg?v=1785804229","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/proof-complexity-generators-paperback-softback-9781009611701","provider":"Freshly Printed Books","version":"1.0","type":"link"}