Proof Complexity Generators
by
Jan Krajicek
Book Details
Format
Paperback / Softback
Book Series
London Mathematical Society Lecture Note Series
ISBN-10
1009611704
ISBN-13
9781009611701
Publisher
Cambridge University Press
Imprint
Cambridge University Press
Country of Manufacture
GB
Country of Publication
GB
Publication Date
Jun 26th, 2025
Print length
134 Pages
Weight
206 grams
Dimensions
22.80 x 15.30 x 0.90 cms
Product Classification:
Mathematical logicAlgebraMathematical theory of computation
Ksh 8,100.00
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This book presents a state-of-the-art theory in the field of proof complexity, aiming to construct hard propositional tautologies needed to solve the P vs. NP problem in the negative. The theory is introduced step by step, starting with the historic background, and several potential new avenues of research are highlighted.
The P vs. NP problem is one of the fundamental problems of mathematics. It asks whether propositional tautologies can be recognized by a polynomial-time algorithm. The problem would be solved in the negative if one could show that there are propositional tautologies that are very hard to prove, no matter how powerful the proof system you use. This is the foundational problem (the NP vs. coNP problem) of proof complexity, an area linking mathematical logic and computational complexity theory. Written by a leading expert in the field, this book presents a theory for constructing such hard tautologies. It introduces the theory step by step, starting with the historic background and a motivational problem in bounded arithmetic, before taking the reader on a tour of various vistas of the field. Finally, it formulates several research problems to highlight new avenues of research.
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