Bounded variability of metric temporal logic

Carlo A. Furia; Paola Spoletini

doi:10.1007/s10472-016-9532-8

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Annals of Mathematics and Artificial Intelligence

August 2017, Volume 80, Issue 3–4, pp 283–316

Bounded variability of metric temporal logic

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Carlo A. FuriaEmail author
Paola Spoletini

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Article

First Online:: 13 December 2016

DOI: 10.1007/s10472-016-9532-8

Cite this article as:: Furia, C.A. & Spoletini, P. Ann Math Artif Intell (2017) 80: 283. doi:10.1007/s10472-016-9532-8

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Abstract

Deciding validity of Metric Temporal Logic (MTL) formulas is generally very complex and even undecidable over dense time domains; bounded variability is one of the several restrictions that have been proposed to bring decidability back. A temporal model has bounded variability if no more than v events occur over any time interval of length V, for constant parameters v and V. Previous work has shown that MTL validity over models with bounded variability is less complex—and often decidable—than MTL validity over unconstrained models. This paper studies the related problem of deciding whether an MTL formula has intrinsic bounded variability, that is whether it is satisfied only by models with bounded variability. The results of the paper are mainly negative: over dense time domains, the problem is mostly undecidable (even if with an undecidability degree that is typically lower than deciding validity); over discrete time domains, it is decidable with the same complexity as deciding validity. As a partial complement to these negative results, the paper also identifies MTL fragments where deciding bounded variability is simpler than validity, which may provide for a reduction in complexity in some practical cases.

Keywords

Metric temporal logic Bounded variability Decidability and complexity

Mathematics Subject Classification (2010)

03B70 03B44

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Authors and Affiliations

Carlo A. Furia
- 1
Email authorView author's OrcID profile
Paola Spoletini
- 2

1.Department of Computer Science and EngineeringChalmers University of TechnologyGothenburgSweden
2.Department of Software Engineering and Game DevelopmentKennesaw State UniversityKennesawUSA

Bounded variability of metric temporal logic

Abstract

Keywords

Mathematics Subject Classification (2010)

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