## Real-time logics: complexity and expressiveness (1993)

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Venue: | INFORMATION AND COMPUTATION |

Citations: | 202 - 16 self |

### BibTeX

@ARTICLE{Alur93real-timelogics:,

author = {Rajeev Alur and Thomas A. Henzinger},

title = {Real-time logics: complexity and expressiveness},

journal = {INFORMATION AND COMPUTATION},

year = {1993},

volume = {104},

pages = {390--401}

}

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### Abstract

The theory of the natural numbers with linear order and monadic predicates underlies propositional linear temporal logic. To study temporal logics that are suitable for reasoning about real-time systems, we combine this classical theory of in nite state sequences with a theory of discrete time, via a monotonic function that maps every state to its time. The resulting theory of timed state sequences is shown to be decidable, albeit nonelementary, and its expressive power is characterized by! -regular sets. Several more expressive variants are proved to be highly undecidable. This framework allows us to classify a wide variety of real-time logics according to their complexity and expressiveness. Indeed, it follows that most formalisms proposed in the literature cannot be decided. We are, however, able to identify two elementary real-time temporal logics as expressively complete fragments of the theory of timed state sequences, and we present tableau-based decision procedures for checking validity. Consequently, these two formalisms are well-suited for the speci cation and veri cation of real-time systems.