Journal of the ACM (JACM)
Many hard examples for resolution
Journal of the ACM (JACM)
Noise strategies for improving local search
AAAI '94 Proceedings of the twelfth national conference on Artificial intelligence (vol. 1)
GRASP—a new search algorithm for satisfiability
Proceedings of the 1996 IEEE/ACM international conference on Computer-aided design
A Computing Procedure for Quantification Theory
Journal of the ACM (JACM)
A Machine-Oriented Logic Based on the Resolution Principle
Journal of the ACM (JACM)
A machine program for theorem-proving
Communications of the ACM
Exponential Separations between Restricted Resolution and Cutting Planes Proof Systems
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
On the validity and complexity of bounded resolution
STOC '75 Proceedings of seventh annual ACM symposium on Theory of computing
The intractability of resolution (complexity)
The intractability of resolution (complexity)
Ten challenges in propositional reasoning and search
IJCAI'97 Proceedings of the 15th international joint conference on Artifical intelligence - Volume 1
Boundary Points and Resolution
SAT '09 Proceedings of the 12th International Conference on Theory and Applications of Satisfiability Testing
A new incomplete method for CSP inconsistency checking
AAAI'08 Proceedings of the 23rd national conference on Artificial intelligence - Volume 1
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We introduce a new method for checking satisfiability of conjunctive normal forms (CNFs). The method is based on the fact that if no clause of a CNF contains a satisfying assignment in its 1-neighborhood, then this CNF is unsatisfiable. (The 1-neighborhood of a clause is the set of all assignments satisfying only one literal of this clause.) The idea of 1-neighborhood exploration allows one to prove unsatisfiability without generating an empty clause. The reason for avoiding the generation of an empty clause is that we believe that no deterministic algorithm can efficiently reach a global goal (deducing an empty clause) using an inherently local operation (resolution). At the same time, when using 1-neighborhood exploration, a global goal is replaced with a set of local subgoals, which makes it possible to optimize steps of the proof. We introduce two proof systems formalizing 1-neighborhood exploration. An interesting open question is whether there exists a class of CNFs for which the introduced systems have proofs that are exponentially shorter than the ones that can be obtained by general resolution.