Generalized Modal Satisfiability

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

It is well known that modal satisfiability is PSPACE-complete (Ladner 1977). However, the complexity may decrease if we restrict the set of propositional operators used. Note that there exist an infinite number of propositional operators, since a propositional operator is simply a Boolean function. We completely classify the complexity of modal satisfiability for every finite set of propositional operators, i.e., in contrast to previous work, we classify an infinite number of problems. We show that, depending on the set of propositional operators, modal satisfiability is PSPACE-complete, coNP-complete, or in P. We obtain this trichotomy not only for modal formulas, but also for their more succinct representation using modal circuits. We consider both the uni-modal and the multi-modal case, and study the dual problem of validity as well.
32 pages, 3 figures. Some of the results appeared in STACS 2006

Keywords

Computational Complexity, Logic in Computer Science

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/212385

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0804.2729
 http://arxiv.org/abs/0804.2729

Collections

arXiv