Bounded Arithmetic, Propositional Logic and Complexity Theory [Hardcover]

Discusses the deep connections between logic and complexity theory, and lists a number of intriguing open problems.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.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.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 independenl.