Resolution for quantified Boolean formulas
Information and Computation
A sharp threshold in proof complexity
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Real-Time Database and Information
Real-Time Database and Information
Complexity of Finding Short Resolution Proofs
MFCS '97 Proceedings of the 22nd International Symposium on Mathematical Foundations of Computer Science
Minimum Propositional Proof Length is NP-Hard to Linearly Approximate
MFCS '98 Proceedings of the 23rd International Symposium on Mathematical Foundations of Computer Science
Lower Bounds for Propositional Proofs and Independence Results in Bounded Arithmetic
ICALP '96 Proceedings of the 23rd International Colloquium on Automata, Languages and Programming
Combining Logic and Optimization in Cutting Plane Theory
FroCoS '00 Proceedings of the Third International Workshop on Frontiers of Combining Systems
Intriactability of Read-Once Resolution
SCT '95 Proceedings of the 10th Annual Structure in Complexity Theory Conference (SCT'95)
Simplified and improved resolution lower bounds
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Time bounded random access machines
Journal of Computer and System Sciences
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This paper is concerned with the design of polynomial time algorithms to determine the shortest length, tree-like resolution refutation proofs for 2SAT and Q2SAT (Quantified 2SAT) clausal systems. Determining the shortest length resolution refutation has been shown to be NP-complete, even for HornSAT systems (for both tree-like and dag-like proofs); in fact obtaining even a linear approximation for such systems is NP-Hard. In this paper we demonstrate the existence of simple and efficient algorithms for the problem of determining the exact number of steps in the minimum length tree-like resolution refutation proof of a 2SAT or Q2SAT clausal system. To the best of our knowledge, our results are the first of their kind.