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  3. Bounded Arithmetic, Propositional Logic and Complexity Theory
  • Cited by 213
  • Jan Krajicek, Academy of Sciences of the Czech Republic, Prague
Publisher:
Cambridge University Press
Online publication date:
December 2009
Print publication year:
1995
Online ISBN:
9780511529948
DOI:
https://doi.org/10.1017/CBO9780511529948
Subjects:
Mathematics (general), Mathematics, Algorithmics, Complexity, Computer Algebra, Computational Geometry, Logic, Categories and Sets, Computer Science
Series:
Encyclopedia of Mathematics and its Applications (60)
Information

Book description

This book presents an up-to-date, unified treatment of research in bounded arithmetic and complexity of propositional logic, with emphasis on independence proofs and lower bound proofs. The author discusses the deep connections between logic and complexity theory and lists a number of intriguing open problems. An introduction to the basics of logic and complexity theory is followed by discussion of important results in propositional proof systems and systems of bounded arithmetic. More advanced topics are then treated, including polynomial simulations and conservativity results, various witnessing theorems, the translation of bounded formulas (and their proofs) into propositional ones, the method of random partial restrictions and its applications, direct independence proofs, complete systems of partial relations, lower bounds to the size of constant-depth propositional proofs, the method of Boolean valuations, the issue of hard tautologies and optimal proof systems, combinatorics and complexity theory within bounded arithmetic, and relations to complexity issues of predicate calculus. Students and researchers in mathematical logic and complexity theory will find this comprehensive treatment an excellent guide to this expanding interdisciplinary area.

Reviews

‘This interesting book provides a brisk account of current research in bounded arithmetic and the complexity of propositional logic.’

Source: Mathematika

‘It can be strongly recommended especially to mathematicians and computer scientists working in the field and to graduate students.’

Source: European Mathematical Society Newsletter

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