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Bounded Arithmetic, Propositional Logic and Complexity Theory
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  • Cited by 74
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    Krajíček, Jan 2018. Randomized feasible interpolation and monotone circuits with a local oracle. Journal of Mathematical Logic, Vol. 18, Issue. 02, p. 1850012.

    Buss, Sam 2017. Uniform proofs of ACC representations. Archive for Mathematical Logic, Vol. 56, Issue. 5-6, p. 639.

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    Beckmann, Arnold and Buss, Sam 2017. The NP Search Problems of Frege and Extended Frege Proofs. ACM Transactions on Computational Logic, Vol. 18, Issue. 2, p. 1.

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    Beyersdorff, Olaf and Pich, Ján 2016. Understanding Gentzen and Frege Systems for QBF. p. 146.

    Garlík, Michal 2016. Construction of models of bounded arithmetic by restricted reduced powers. Archive for Mathematical Logic, Vol. 55, Issue. 5-6, p. 625.

    Atserias, Albert and Müller, Moritz 2015. Partially definable forcing and bounded arithmetic. Archive for Mathematical Logic, Vol. 54, Issue. 1-2, p. 1.

    Garlík, Michal 2015. A new proof of Ajtai’s completeness theorem for nonstandard finite structures. Archive for Mathematical Logic, Vol. 54, Issue. 3-4, p. 413.

    Razborov, Alexander 2015. Pseudorandom generators hard for k-DNF resolution and polynomial calculus resolution. Annals of Mathematics, Vol. 181, Issue. 2, p. 415.

  • Jan Krajicek, Academy of Sciences of the Czech Republic, Prague

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    Bounded Arithmetic, Propositional Logic and Complexity Theory
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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.


‘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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