Krajíček, Jan creator text bibliography enk Cambridge, UK New York Cambridge University Press 2011 monographic eng

print

xvi, 247 p. : ill. ; 23 cm. "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"-- Jan Krajíček. Includes bibliographical references (p. 236-242) and indexes. Computational complexity Random variables Mathematical analysis QA267.7 .K73 2011 511.36 9780521154338 0521154332 (pbk.) 2010036194 http://assets.cambridge.org/97805211/54338/cover/9780521154338.jpg http://assets.cambridge.org/97805211/54338/cover/9780521154338.jpg DLC 100823 20150408114018.0 16429416