Forcing with Random Variables and Proof Complexity

Name: Forcing with Random Variables and Proof Complexity
Price: 146.88 AUD
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ISBN: 9780521154338

Jan Krajíček (Charles University, Prague)

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English

Cambridge University Press
23 December 2010

Mathematics & Sciences; Mathematical logic; Mathematical theory of computation

Series: London Mathematical Society Lecture Note Series

This book introduces a new approach to building models of bounded arithmetic, with techniques drawn from recent results in computational complexity. Propositional proof systems and bounded arithmetics are closely related. In particular, proving lower bounds on the lengths of proofs in propositional proof systems is equivalent to constructing certain extensions of models of bounded arithmetic. This offers a clean and coherent framework for thinking about lower bounds for proof lengths, and it has proved quite successful in the past. This book outlines a brand new method for constructing models of bounded arithmetic, thus for proving independence results and establishing lower bounds for proof lengths. The models are built from random variables defined on a sample space which is a non-standard finite set and sampled by functions of some restricted computational complexity. It will appeal to anyone interested in logical approaches to fundamental problems in complexity theory.

By: Jan Krajíček (Charles University Prague)
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Volume: 382
Dimensions: Height: 228mm, Width: 152mm, Spine: 15mm
Weight: 380g
ISBN: 9780521154338
ISBN 10: 0521154332
Series: London Mathematical Society Lecture Note Series
Pages: 264
Publication Date: 23 December 2010
Audience: Professional and scholarly , Undergraduate
Format: Paperback
Publisher's Status: Active

Jan Kraji ek is a Professor of Mathematical Logic at Charles University in Prague. He is currently also affiliated with the Academy of Sciences of the Czech Republic.

Reviews for Forcing with Random Variables and Proof Complexity

Jan Krajicek is the leading expert on these problems and in this book he provides a new approach to builing models of bounded arithmetic which combines methods and techniques from model theory, forcing and computational complexity. Personally, I find Krajicek's approach a highly stimulating collage of ideas. I recommend this book strongly to anyone interested in logical approaches to fundamental problems in complexity theory. Soren M. Riis for Mathematical Reviews