Bounded Arithmetic, Propositional Logic and Complexity Theory by Jan Krajicek
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Bounded Arithmetic, Propositional Logic and Complexity Theory
By Jan Krajicek

Bounded Arithmetic, Propositional Logic and Complexity Theory

By (author) See other recent books by Jan Krajicek
Series edited by Gian-Carlo Rota See other recent books by Gian-Carlo Rota See other recent books by B. Doran
Format: Hardback

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Bounded Arithmetic, Propositional Logic and Complexity Theory by Jan Krajicek

Book Description

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.

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Book Details

ISBN: 9780521452052
ISBN-10: 0521452058
Format: Hardback
(228mm x 152mm x 24mm)
Pages: 360
Imprint: Cambridge University Press
Publisher: Cambridge University Press
Publish Date: 24-Nov-1995
Country of Publication: United Kingdom

Books By Author Jan Krajicek

Forcing with Random Variables and Proof Complexity by Jan Krajicek Forcing with Random Variables and Proof Complexity, Paperback (December 2010)

A model-theoretic approach to bounded arithmetic and propositional proof complexity.

Arithmetic, Proof Theory and Computational Complexity by Jan Krajicek Arithmetic, Proof Theory and Computational Complexity, Hardback (May 1993)

This book principally concerns the area of "Logical Complexity Theory", the study of bounded arithmetic, propositional proof systems, length of proof, etc and relations to computational complexity theory. This includes an open problem list of 7 fundamental and 39 technical questions together with a bibliography of references.

» View all books by Jan Krajicek

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