Some Recent Results in Metric Temporal Logic

Authors:
Joël Ouaknine;James Worrell
Affiliations:
Oxford University Computing Laboratory, UK;Oxford University Computing Laboratory, UK
Venue:
FORMATS '08 Proceedings of the 6th international conference on Formal Modeling and Analysis of Timed Systems
Year:
2008

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Abstract

Metric Temporal Logic (MTL) is a widely-studied real-time extension of Linear Temporal Logic. In this paper we survey results about the complexity of the satisfiability and model checking problems for fragments of MTLwith respect to different semantic models. We show that these fragments have widely differing complexities: from polynomial space to non-primitive recursive and even undecidable. However we show that the most commonly occurring real-time properties, such as invariance and bounded response, can be expressed in fragments of MTLfor which model checking, if not satisfiability, can be decided in polynomial or exponential space.