@article{4589, 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.}, author = {Alur, Rajeev and Henzinger, Thomas A}, issn = {0890-5401}, journal = {Information and Computation}, number = {1}, pages = {35 -- 77}, publisher = {Elsevier}, title = {{Real-time logics: Complexity and expressiveness}}, doi = {10.1006/inco.1993.1025}, volume = {104}, year = {1993}, }