Journal of the ACM (JACM)
Some results and experiments in programming techniques for propositional logic
Computers and Operations Research - Special issue: Applications of integer programming
A hierarchy of tractable satisfiability problems
Information Processing Letters
A Computing Procedure for Quantification Theory
Journal of the ACM (JACM)
Mechanical Theorem-Proving by Model Elimination
Journal of the ACM (JACM)
A Simplified Format for the Model Elimination Theorem-Proving Procedure
Journal of the ACM (JACM)
A Linear Format for Resolution With Merging and a New Technique for Establishing Completeness
Journal of the ACM (JACM)
A Unifying View of Some Linear Herbrand Procedures
Journal of the ACM (JACM)
An Implementation of the Model Elimination Proof Procedure
Journal of the ACM (JACM)
Renaming a Set of Clauses as a Horn Set
Journal of the ACM (JACM)
A machine program for theorem-proving
Communications of the ACM
Parallel cooperative propositional theorem proving
Annals of Mathematics and Artificial Intelligence
A propositional theorem prover to solve planning and other problems
Annals of Mathematics and Artificial Intelligence
Lemma and cut strategies for propositional model elimination
Annals of Mathematics and Artificial Intelligence
The Use of Lemmas in the Model Elimination Procedure
Journal of Automated Reasoning
CSL '92 Selected Papers from the Workshop on Computer Science Logic
Caching and Lemmaizing in Model Elimination Theorem Provers
CADE-11 Proceedings of the 11th International Conference on Automated Deduction: Automated Deduction
The Search Efficiency of Theorem Proving Strategies
CADE-12 Proceedings of the 12th International Conference on Automated Deduction
CADE-13 Proceedings of the 13th International Conference on Automated Deduction: Automated Deduction
SATO: An Efficient Propositional Prover
CADE-14 Proceedings of the 14th International Conference on Automated Deduction
Automated theorem proving: A logical basis (Fundamental studies in computer science)
Automated theorem proving: A logical basis (Fundamental studies in computer science)
Parallel cooperative propositional theorem proving
Annals of Mathematics and Artificial Intelligence
A propositional theorem prover to solve planning and other problems
Annals of Mathematics and Artificial Intelligence
Lemma and cut strategies for propositional model elimination
Annals of Mathematics and Artificial Intelligence
Conditional Pure Literal Graphs
IJCAR '01 Proceedings of the First International Joint Conference on Automated Reasoning
Lean clause-sets: generalizations of minimally unsatisfiable clause-sets
Discrete Applied Mathematics - The renesse issue on satisfiability
Persistent and Quasi-Persistent Lemmas in Propositional Model Elimination
Annals of Mathematics and Artificial Intelligence
Annals of Mathematics and Artificial Intelligence
Another look at graph coloring via propositional satisfiability
Discrete Applied Mathematics
A decision-making procedure for resolution-based SAT-solvers
SAT'08 Proceedings of the 11th international conference on Theory and applications of satisfiability testing
Searching for autarkies to trim unsatisfiable clause sets
SAT'08 Proceedings of the 11th international conference on Theory and applications of satisfiability testing
An overview of parallel SAT solving
Constraints
Constraint Satisfaction Problems in Clausal Form I: Autarkies and Deficiency
Fundamenta Informaticae
Hi-index | 0.00 |
Goal-sensitive resolution methods, such as Model Elimination, have been observed to have a higher degree of search redundancy than model-search methods. Therefore, resolution methods have not been seen in high-performance propositional satisfiability testers. A method to reduce search redundancy in goal-sensitive resolution methods is introduced. The idea at the heart of the method is to attempt to construct a refutation and a model simultaneously and incrementally, based on subsearch outcomes. The method exploits the concept of ’autarky‘, which can be informally described as a ’self-sufficient‘ model for some clauses, but which does not affect the remaining clauses of the formula. Incorporating this method into Model Elimination leads to an algorithm called Modoc. Modoc is shown, both analytically and experimentally, to be faster than Model Elimination by an exponential factor. Modoc, unlike Model Elimination, is able to find a model if it fails to find a refutation, essentially by combining autarkies. Unlike the pruning strategies of most refinements of resolution, autarky-related pruning does not prune any successful refutation; it only prunes attempts that ultimately will be unsuccessful; consequently, it will not force the underlying Modoc search to find an unnecessarily long refutation. To prove correctness and other properties, a game characterization of refutation search is introduced, which demonstrates some symmetries in the search for a refutation and the search for a model. Experimental data is presented on a variety of formula classes, comparing Modoc with Model Elimination and model-search algorithms. On random formulas, model-search methods are faster than Modoc, whereas Modoc is faster on structured formulas, including those derived from a circuit-testing application. Considerations for first-order refutation methods are discussed briefly.