Vestnik TVGU. Seriya: Prikladnaya Matematika [Herald of Tver State University. Series: Applied Mathematics]
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Vestnik TVGU. Seriya: Prikladnaya Matematika [Herald of Tver State University. Series: Applied Mathematics], 2007, Issue 5, Pages 5–17 (Mi vtpmk419)  

This article is cited in 2 scientific papers (total in 2 papers)

Mathematical Foundations of Computer Science

The complexity of the constant fragment of propositional dynamic logic

M. N. Rybakov

Tver State University, Department of Mathematics, Tver
Citations (2)
Abstract: The main result of the paper is in that the variable-free fragments of the logics ${\ bf K}^\ ast$ (with ${\ bf K}$-modality and its ‘reflexive and transitive closure’), PDL, and some others are EXPTIME-complete. In the proof some quite general idea how to construct a polynomial reduction of propositional logic to its $n$-variable (and even variable-free in the case of ${\ bf K}^\ ast$ and PDL) fragment is presented. As a corollary we obtain that the one-variable fragments of logics of knowledge with common knowledge operator are EXPTIME-complete.
Keywords: propositional dynamic logic, complexity, EXPTIME-completeness, decision problem.
Funding agency Grant number
Russian Foundation for Basic Research 06--06--80380
06--01--72555--НЦНИЛ_а
07--06--00318
Received: 15.05.2007
Revised: 14.06.2007
Bibliographic databases:
Document Type: Article
UDC: 517.11
Language: Russian
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  • This publication is cited in the following 2 articles:
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    Vestnik TVGU. Seriya: Prikladnaya Matematika [Herald of Tver State University. Series: Applied Mathematics]
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