01834nmm a2200277 u 4500001001200000003002700012005001700039007002400056008004100080020001800121050001200139100001800151245007300169260004800242300002700290653002900317653001700346653003700363700002900400041001900429989003200448490002600480856006300506082001100569520097600580EB001888159EBX0100000000000000105152000000000000000.0cr|||||||||||||||||||||200106 ||| eng a9780511676277 4aQA267.71 aCook, Stephen00aLogical foundations of proof complexitycStephen Cook, Phuong Nguyen aCambridgebCambridge University Pressc2010 axv, 479 pagesbdigital aComputational complexity aProof theory aLogic, Symbolic and mathematical1 aNguyen, Phuonge[author]07aeng2ISO 639-2 bCBOaCambridge Books Online0 aPerspectives in logic40uhttps://doi.org/10.1017/CBO9780511676277xVerlag3Volltext0 a511.36 aThis book treats bounded arithmetic and propositional proof complexity from the point of view of computational complexity. The first seven chapters include the necessary logical background for the material and are suitable for a graduate course. Associated with each of many complexity classes are both a two-sorted predicate calculus theory, with induction restricted to concepts in the class, and a propositional proof system. The complexity classes range from AC0 for the weakest theory up to the polynomial hierarchy. Each bounded theorem in a theory translates into a family of (quantified) propositional tautologies with polynomial size proofs in the corresponding proof system. The theory proves the soundness of the associated proof system. The result is a uniform treatment of many systems in the literature, including Buss's theories for the polynomial hierarchy and many disparate systems for complexity classes such as AC0, AC0(m), TC0, NC1, L, NL, NC, and P.