Search results for "Boolean satisfiability problem"
showing 2 items of 12 documents
On the satisfiability problem for fragments of two-variable logic with one transitive relation
2019
Abstract We study the satisfiability problem for two-variable first-order logic over structures with one transitive relation. We show that the problem is decidable in 2-NExpTime for the fragment consisting of formulas where existential quantifiers are guarded by transitive atoms. As this fragment enjoys neither the finite model property nor the tree model property, to show decidability we introduce a novel model construction technique based on the infinite Ramsey theorem. We also point out why the technique is not sufficient to obtain decidability for the full two-variable logic with one transitive relation; hence, contrary to our previous claim, [FO$^2$ with one transitive relation is deci…
Some Computational Aspects of DISTANCE-SAT
2007
In many AI fields, one must face the problem of finding a solution that is as close as possible to a given configuration. This paper addresses this problem in a propositional framework. We introduce the decision problem distance-sat, which consists in determining whether a propositional formula admits a model that disagrees with a given partial interpretation on at most d variables. The complexity of distance-sat and of several restrictions of it are identified. Two algorithms based on the well-known Davis/Logemann/Loveland search procedure for the satisfiability problem sat are presented so as to solve distance-sat for CNF formulas. Their computational behaviors are compared with the ones …