Forcing with Random Variables and Proof Complexity (London Mathematical Society Lecture Note Series, Series Number 382) - Softcover

Krajíček, Jan

Softcover

ISBN 10: 0521154332 ISBN 13: 9780521154338

Publisher: Cambridge University Press, 2011

Synopsis

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.

About this title

Book Description

Aimed at researchers and graduate students in mathematics and theoretical computer science, who are interested in logical approaches to fundamental problems of computational complexity theory, and of proof complexity in particular.

About the Author

Jan Krajíček 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.

Edition details

• Publisher: Cambridge University Press
• Publication date: 2011
• ISBN 10: 0521154332
• ISBN 13: 9780521154338
• Binding: Paperback
• Language: English
• Edition number: 1
• Number of pages: 264