Real-time logics: Complexity and expressiveness Journal Article

Author(s): Alur, Rajeev; Henzinger, Thomas A
Article Title: Real-time logics: Complexity and expressiveness
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 infinite 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 ω-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 specification and verification of real-time systems. Copyright © 1993 Academic Press. All rights reserved.
Journal Title: Information and Computation
Volume: 104
Issue 1
ISSN: 0890-5401
Publisher: Elsevier  
Date Published: 1993-05-01
Start Page: 35
End Page: 77
DOI: 10.1006/inco.1993.1025
Open access: no
IST Austria Authors
  1. Thomas A. Henzinger
    415 Henzinger
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