Proof Complexity Generators (Paperback)

Jan Krajicek

ISBN 10: 1009611704 / ISBN 13: 9781009611701

Published by Cambridge University Press, Cambridge, 2025

About this Item

Paperback. 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. 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. This item is printed on demand. Shipping may be from multiple locations in the US or from the UK, depending on stock availability.

Seller Inventory # 9781009611701

Bibliographic Details

• Title: Proof Complexity Generators (Paperback)
• Publisher: Cambridge University Press, Cambridge
• Publication Date: 2025
• Language: English
• ISBN 10: 1009611704
• ISBN 13: 9781009611701
• Binding: Paperback
• Condition: new

About this title

Synopsis

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.

About the Author

Jan Krajíček is Professor of Mathematical Logic at Charles University, Prague. A member of the Learned Society of the Czech Republic and the Academia Europaea, he has previously published three books with Cambridge University Press (1995, 2011 and 2019).