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200106  eng 
020 


a 9780511676277

050 

4 
a QA267.7

100 
1 

a Cook, Stephen

245 
0 
0 
a Logical foundations of proof complexity
c Stephen Cook, Phuong Nguyen

260 


a Cambridge
b Cambridge University Press
c 2010

300 


a xv, 479 pages
b digital

653 


a Computational complexity

653 


a Proof theory

653 


a Logic, Symbolic and mathematical

700 
1 

a Nguyen, Phuong
e [author]

041 
0 
7 
a eng
2 ISO 6392

989 


b CBO
a Cambridge Books Online

490 
0 

a Perspectives in logic

856 
4 
0 
u https://doi.org/10.1017/CBO9780511676277
x Verlag
3 Volltext

082 
0 

a 511.36

520 


a This 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 twosorted 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.
