Proof Complexity Generators
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.
- Presents an advanced proof complexity approach to the NP vs. coNP problem, including perspectives from both mathematical logic and computational complexity theory
- Introduces the theory step by step starting with the historic background and a motivational problem in bounded arithmetic
- Formulates a number of research problems pointing to possible further developments of the theory
Product details
August 2025Paperback
9781009611701
143 pages
229 × 152 mm
Not yet published - available from August 2025
Table of Contents
- 1. Introduction
- 2. The dWPHP problem
- 3. τ-formulas and generators
- 4. The stretch
- 5. Nisan-Wigderson generator
- 6. Gadget generator
- 7. The case of ER
- 8. Consistency results
- 9. Contexts
- 10. Further research
- Special symbols
- References
- Index.