A Does Treewidth Help in Modal Satisfiability?
نویسنده
چکیده
Many tractable algorithms for solving the Constraint Satisfaction Problem (Csp) have been developed using the notion of the treewidth of some graph derived from the input Csp instance. In particular, the incidence graph of the Csp instance is one such graph. We introduce the notion of an incidence graph for modal logic formulas in a certain normal form. We investigate the parameterized complexity of modal satisfiability with the modal depth of the formula and the treewidth of the incidence graph as parameters. For various combinations of Euclidean, reflexive, symmetric and transitive models, we show either that modal satisfiability is Fixed Parameter Tractable (Fpt), or that it is W[1]-hard. In particular, modal satisfiability in general models is Fpt, while it is W[1]-hard in transitive models. As might be expected, modal satisfiability in transitive and Euclidean models is Fpt.
منابع مشابه
Does Treewidth Help in Modal Satisfiability? - (Extended Abstract)
Many tractable algorithms for solving the Constraint Satisfaction Problem (Csp) have been developed using the notion of the treewidth of some graph derived from the input Csp instance. In particular, the incidence graph of the Csp instance is one such graph. We introduce the notion of an incidence graph for modal logic formulae in a certain normal form. We investigate the parameterized complexi...
متن کاملPDL with Intersection and Converse is 2EXP-complete
We study the complexity of satisfiability in the expressive extension ICPDL of PDL (Propositional Dynamic Logic), which admits intersection and converse as program operations. Our main result is containment in 2EXP, which improves the previously known non-elementary upper bound and implies 2EXPcompleteness due to an existing lower bound for PDL with intersection. The proof proceeds by showing t...
متن کاملSmall Resolution Proofs for QBF using Dependency Treewidth
In spite of the close connection between the evaluation of quantified Boolean formulas (QBF) and propositional satisfiability (SAT), tools and techniques which exploit structural properties of SAT instances are known to fail for QBF. This is especially true for the structural parameter treewidth, which has allowed the design of successful algorithms for SAT but cannot be straightforwardly appli...
متن کاملThe Computational Complexity of the Satisfiability of Modal Horn Clauses for Modal Propositional Logics
This paper presents complexity results about the satisfiability ofmodal Horn clauses for several modal propositional logics. Almost all these results are negative in the sense that restricting the input formula to modal Horn clauses does not decrease the inherent complexity of the satisfiability problem. We first show that, when restricted to modal Horn clauses, the satisfiability problem for a...
متن کاملEncoding Treewidth into SAT
One of the most important structural parameters of graphs is treewidth, a measure for the “tree-likeness” and thus in many cases an indicator for the hardness of problem instances. The smaller the treewidth, the closer the graph is to a tree and the more efficiently the underlying instance often can be solved. However, computing the treewidth of a graph is NP-hard in general. In this paper we p...
متن کامل