Results 221 to 230 of about 2,128,058 (249)

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.
openaire   +2 more sources

Twelve Problems in Proof Complexity

2008
Proof complexity is a research area that studies the concept of complexity from the point of view of logic. Although it is very much connected with computational complexity, the goals are different. In proof complexity we are studying the question how difficult is to prove a theorem?
openaire   +2 more sources

Jump Operators, Interactive Proofs and Proof Complexity Generators

2024 IEEE 65th Annual Symposium on Foundations of Computer Science (FOCS)
A jump operator J in proof complexity is a function such that for any proof system P, J(P) is a proof system that P cannot simulate. Some candidate jump operators were proposed by Krajicek and Pudlak [63] and Krajicek [57], but it is an open problem whether computable jump operators exist or not.
exaly   +3 more sources

Proof Complexity of Pigeonhole Principles

2002
The pigeonhole principle asserts that there is no injective mapping from m pigeons to n holes as long as m > n. It is amazingly simple, expresses one of the most basic primitives in mathematics and Theoretical Computer Science (counting) and, for these reasons, is probably the most extensively studied combinatorial principle.
openaire   +1 more source

Proofs, Programs and Abstract Complexity

2007
Axiom systems are ubiquitous in mathematical logic, one famous example being first order Peano Arithmetic. Foundational questions asked about axiom systems comprise analysing their provable consequences, describing their class of provable recursive functions (i.e.
openaire   +1 more source

Substitution and Propositional Proof Complexity

Outstanding Contributions To Logic, 2022
Sam Buss
exaly  

Computational Complexity and Mathematical Proofs

2001
This paper discusses howthe major computational complexity classes, P, NP and PSPACE, capture different computational properties of mathematical proofs and reveal newq uantitative aspects of mathematics.
openaire   +2 more sources

Termination Proofs and Complexity Certification

2001
We show that simple structural conditions on proofs of convergence of equational programs, in the intrinsic-theories verification framework of [16], correspond to resource bounds on program execution. These conditions may be construed as reflecting finitistic-predicative reasoning.
openaire   +1 more source

Computational and Proof Complexity of Partial String Avoidability

ACM Transactions on Computation Theory, 2021
Alexander Okhotin, Dmitry Itsykson
exaly  

New Resolution-Based QBF Calculi and Their Proof Complexity

ACM Transactions on Computation Theory, 2019
Olaf Beyersdorff, Leroy Chew, Mikoláš Janota   +2 more
exaly