David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Cambridge University Press (1995)
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.
|Keywords||Constructive mathematics Proposition (Logic Computational complexity|
|Categories||categorize this paper)|
|Buy the book||$95.00 used (50% off) $148.80 new (22% off) $189.99 direct from Amazon Amazon page|
|Call number||QA9.56.K73 1995|
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Citations of this work BETA
Sebastian Müller & Iddo Tzameret (2014). Short Propositional Refutations for Dense Random 3CNF Formulas. Annals of Pure and Applied Logic 165 (12):1864-1918.
Mihai Ganea (2010). Two (or Three) Notions of Finitism. Review of Symbolic Logic 3 (1):119-144.
Olaf Beyersdorff, Arne Meier, Sebastian Müller, Michael Thomas & Heribert Vollmer (2011). Proof Complexity of Propositional Default Logic. Archive for Mathematical Logic 50 (7-8):727-742.
Fernando Ferreira & António Marques (1998). Extracting Algorithms From Intuitionistic Proofs. Mathematical Logic Quarterly 44 (2):143-160.
Samuel R. Buss (1997). Bounded Arithmetic, Cryptography and Complexity. Theoria 63 (3):147-167.
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