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Logic Journal of IGPL
Article . 2018 . Peer-reviewed
License: OUP Standard Publication Reuse
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https://dx.doi.org/10.48550/ar...
Article . 2019
License: arXiv Non-Exclusive Distribution
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Complexity and expressivity of propositional dynamic logics with finitely many variables

Authors: Dmitry Shkatov; Mikhail N. Rybakov; Mikhail N. Rybakov;

Complexity and expressivity of propositional dynamic logics with finitely many variables

Abstract

We investigate the complexity of satisfiability for finite-variable fragments of propositional dynamic logics. We consider three formalisms belonging to three representative complexity classes, broadly understood,---regular PDL, which is EXPTIME-complete, PDL with intersection, which is 2EXPTIME-complete, and PDL with parallel composition, which is undecidable. We show that, for each of these logics, the complexity of satisfiability remains unchanged even if we only allow as inputs formulas built solely out of propositional constants, i.e. without propositional variables. Moreover, we show that this is a consequence of the richness of the expressive power of variable-free fragments: for all the logics we consider, such fragments are as semantically expressive as entire logics. We conjecture that this is representative of PDL-style, as well as closely related, logics.

Keywords

FOS: Computer and information sciences, Computer Science - Logic in Computer Science, FOS: Mathematics, Mathematics - Logic, Logic (math.LO), Logic in Computer Science (cs.LO)

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citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
19
Top 10%
Top 10%
Top 10%
Green
hybrid