Short proofs for tricky formulas
Acta Informatica
Unrestricted resolution versus N-resolution
Theoretical Computer Science
Using the Groebner basis algorithm to find proofs of unsatisfiability
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Proof complexity in algebraic systems and bounded depth Frege systems with modular counting
Computational Complexity
Short proofs are narrow—resolution made simple
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Linear gaps between degrees for the polynomial calculus modulo distinct primes
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Lower bounds for the polynomial calculus and the Gröbner basis algorithm
Computational Complexity
Lower bounds for the polynomial calculus
Computational Complexity
Logic for Computer Scientists
Resolution and the Weak Pigeonhole Principle
CSL '97 Selected Papers from the11th International Workshop on Computer Science Logic
Some Consequences of Cryptographical Conjectures for S_2^1 and EF
LCC '94 Selected Papers from the International Workshop on Logical and Computational Complexity
Non-Automatizability of Bounded-Depth Frege Proofs
COCO '99 Proceedings of the Fourteenth Annual IEEE Conference on Computational Complexity
No feasible interpolation for TC/sup 0/-Frege proofs
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
Exponential Separations between Restricted Resolution and Cutting Planes Proof Systems
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Simplified and improved resolution lower bounds
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Short proofs are narrow—resolution made simple
Journal of the ACM (JACM)
An exponential separation between regular and general resolution
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Optimality of size-width tradeoffs for resolution
Computational Complexity
Annals of Mathematics and Artificial Intelligence
Exponential separation between Res(k) and Res(k + 1) for k ≤ &949; logn
Information Processing Letters
Constant-depth Frege systems with counting axioms polynomially simulate Nullstellensatz refutations
ACM Transactions on Computational Logic (TOCL)
Narrow proofs may be spacious: separating space and width in resolution
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Discrete Applied Mathematics
Tight rank lower bounds for the Sherali–Adams proof system
Theoretical Computer Science
Understanding the power of clause learning
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
Exponential separation between Res (k) and Res(k+1) for k≤εlogn
Information Processing Letters
ACM Transactions on Computation Theory (TOCT)
Optimality of size-degree tradeoffs for polynomial calculus
ACM Transactions on Computational Logic (TOCL)
Pool resolution and its relation to regular resolution and DPLL with clause learning
LPAR'05 Proceedings of the 12th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
Input distance and lower bounds for propositional resolution proof length
SAT'05 Proceedings of the 8th international conference on Theory and Applications of Satisfiability Testing
An improved separation of regular resolution from pool resolution and clause learning
SAT'12 Proceedings of the 15th international conference on Theory and Applications of Satisfiability Testing
Hi-index | 0.00 |
This paper is concerned with the complexity of proofs and of searching for proofs in two propositional proof systems: Resolution and Polynomial Calculus (PC). For the former system we show that the recently proposed algorithm of BenSasson and Wigderson (STOC 99) for searching for proofs cannot give better than weakly exponential performance. This is a consequence of showing optimality of their general relationship referred to as size-width tradeoff. We moreover obtain the optimality of the size-width tradeoff for the widely used restrictions of resolution: regular, Davis-Putnam, negative, positive and linear.As for the second system, we show that the direct translation to polynomials of a CNF formula having short resolution proofs, cannot be refuted in PC with degree less than \math. A consequence of this is that the simulation of resolution by PC of Clegg, Edmonds and Impagliazzo (STOC 92) cannot be improved to better than quasipolynomial in the case we start with small resolution proofs. We conjecture that the simulation of Clegg at al. is optimal.