Bounded arithmetic, propositional logic, and complexity theory
Bounded arithmetic, propositional logic, and complexity theory
A Computing Procedure for Quantification Theory
Journal of the ACM (JACM)
A machine program for theorem-proving
Communications of the ACM
Feasibly constructive proofs and the propositional calculus (Preliminary Version)
STOC '75 Proceedings of seventh annual ACM symposium on Theory of computing
On the automatizability of resolution and related propositional proof systems
Information and Computation
Towards understanding and harnessing the potential of clause learning
Journal of Artificial Intelligence Research
Logical Foundations of Proof Complexity
Logical Foundations of Proof Complexity
Clause-learning algorithms with many restarts and bounded-width resolution
Journal of Artificial Intelligence Research
| Hi-index | 0.89 |
We apply classical proof complexity ideas to transfer lengths-of-proofs lower bounds for a propositional proof system P into examples of hard unsatisfiable formulas for a class Alg(P) of SAT algorithms determined by P. The class Alg(P) contains those algorithms M for which P proves in polynomial size tautologies expressing the soundness of M. For example, the class Alg(F"d) determined by a depth d Frege system contains the commonly considered enhancements of DPLL (even for small d). Exponential lower bounds are known for all F"d. Such results can be interpreted as a form of consistency of PNP. Further we show how the soundness statements can be used to find hard satisfiable instances, if they exist.