David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
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||$84.72 used (56% off) $161.43 new (16% off) $189.99 direct from Amazon Amazon page|
|Call number||QA9.56.K73 1995|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
No references found.
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.
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.
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.
Similar books and articles
Jan Krajíček & Pavel Pudlák (1989). Propositional Proof Systems, the Consistency of First Order Theories and the Complexity of Computations. Journal of Symbolic Logic 54 (3):1063-1079.
Douglas Cenzer & Jeffrey B. Remmel (2006). Complexity, Decidability and Completeness. Journal of Symbolic Logic 71 (2):399 - 424.
Jan Krajiček (1994). Lower Bounds to the Size of Constant-Depth Propositional Proofs. Journal of Symbolic Logic 59 (1):73-86.
Maria Bonet, Toniann Pitassi & Ran Raz (1997). Lower Bounds for Cutting Planes Proofs with Small Coefficients. Journal of Symbolic Logic 62 (3):708-728.
Jan Krajíček (2004). Implicit Proofs. Journal of Symbolic Logic 69 (2):387 - 397.
Samuel R. Buss (1987). Polynomial Size Proofs of the Propositional Pigeonhole Principle. Journal of Symbolic Logic 52 (4):916-927.
Jan Krajicek (2001). Tautologies From Pseudo-Random Generators. Bulletin of Symbolic Logic 7 (2):197-212.
Merlijn Sevenster (2006). On the Computational Consequences of Independence in Propositional Logic. Synthese 149 (2):257 - 283.
Jan Krajíček (1997). Interpolation Theorems, Lower Bounds for Proof Systems, and Independence Results for Bounded Arithmetic. Journal of Symbolic Logic 62 (2):457-486.
Nathan Segerlind (2007). The Complexity of Propositional Proofs. Bulletin of Symbolic Logic 13 (4):417-481.
Added to index2009-01-28
Total downloads10 ( #235,035 of 1,726,249 )
Recent downloads (6 months)1 ( #369,877 of 1,726,249 )
How can I increase my downloads?