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

Book 315 of 387: London Mathematical Society Lecture Notes

Krajicek, Jan

 
9780521154338: Forcing with Random Variables and Proof Complexity: 382 (London Mathematical Society Lecture Note Series, Series Number 382)
Softcover
ISBN 10: 0521154332 ISBN 13: 9780521154338
Publisher: Cambridge University Press, 2010

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.

"synopsis" may belong to another edition of this title.

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.

"About this title" may belong to another edition of this title.

Publisher
Cambridge University Press
Publication date
2010
Language
English
ISBN 10 
0521154332
ISBN 13 
9780521154338
Binding
Paperback
Number of pages
264