Bounded Arithmetic, Propositional Logic and Complexity Theory
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Bounded Arithmetic, Propositional Logic and Complexity Theory by Jan Krajicek
Book DescriptionThis 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 DetailsISBN: 9780521452052
(228mm x 152mm x 24mm)
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, Paperback (December 2010)
A model-theoretic approach to bounded arithmetic and propositional proof complexity.
Arithmetic, Proof Theory and Computational Complexity, Hardback (May 1993)» View all books by Jan Krajicek
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.
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