Encyclopedia of Mathematics and its Applications: Bounded Arithmetic, Propositional Logic and Complexity Theory Series Number 60 (Hardback)
  • Encyclopedia of Mathematics and its Applications: Bounded Arithmetic, Propositional Logic and Complexity Theory Series Number 60 (Hardback)
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Encyclopedia of Mathematics and its Applications: Bounded Arithmetic, Propositional Logic and Complexity Theory Series Number 60 (Hardback)

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£108.00
Hardback 360 Pages / Published: 24/11/1995
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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.

Publisher: Cambridge University Press
ISBN: 9780521452052
Number of pages: 360
Weight: 650 g
Dimensions: 242 x 162 x 27 mm


MEDIA REVIEWS
'This interesting book provides a brisk account of current research in bounded arithmetic and the complexity of propositional logic.' Mathematika
'It can be strongly recommended especially to mathematicians and computer scientists working in the field and to graduate students.' European Mathematical Society Newsletter
"...the author has produced a very good piece of work, which can be strongly recommended to anyone wishing to study the relations between bounded arithmetic and complexity of propositional logic." Constantine Dimitracopoulos
"...a mathematical masterpiece...presents students and researchers with the most important tools, general background and literature references to begin research in this exciting new area in the intersection of mathematical logic, theoretical computer science, and finite combinatorics...a major accomplishment...will play a substantial role in the training of future researchers." Journal of Symbolic Logic

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