Bounded Arithmetic, Propositional Logic and Complexity Theory (Encyclopedia of Mathematics and its Applications)

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9780521452052: Bounded Arithmetic, Propositional Logic and Complexity Theory (Encyclopedia of Mathematics and its Applications)
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This 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 is followed by discussion of important results in propositional proof systems and systems of bounded arithmetic. Then more advanced topics are 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, simple independence proofs, complete systems of partial relations, lower bounds to the size of constant-depth propositional proofs, the approximation method and the method of Boolean valuations, 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 his comprehensive treatment an excellent guide to this expanding interdisciplinary area.

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This book presents an up-to-date, unified treatment of research in in this interdisciplinary subject with emphasis on independence proofs and lower bound proofs. A basic introduction is followed by discussion of important results in propositional proof systems and systems of bounded arithmetic. Then more advanced topics are treated, including Boolean complexity, witnessing theorems, and bounded arithmetic as a system of feasible arguments. Students and researchers in logic and computer science will find this an excellent guide to an expanding area.

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"...the author has produced a very good piece of work, which can be strongly recommended to anyone wishing to study the relations between bounded arithmetic and complexity of propositional logic." Constantine Dimitracopoulos

"...a mathematical masterpiece...presents students and researchers with the most important tools, general background and literature references to begin research in this exciting new area in the intersection of mathematical logic, theoretical computer science, and finite combinatorics...a major accomplishment...will play a substantial role in the training of future researchers." Journal of Symbolic Logic

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Book Description CAMBRIDGE UNIVERSITY PRESS, United Kingdom, 2004. Hardback. Condition: New. Language: English . Brand New Book ***** Print on Demand *****. This 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. Seller Inventory # APC9780521452052

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Book Description CAMBRIDGE UNIVERSITY PRESS, United Kingdom, 2004. Hardback. Condition: New. Language: English . Brand New Book ***** Print on Demand *****.This 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. Seller Inventory # APC9780521452052

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