{"publisher":"Elsevier","month":"05","date_created":"2018-12-11T12:09:38Z","publication_status":"published","issue":"1","publication":"Information and Computation","oa_version":"Published Version","doi":"10.1006/inco.1993.1025","publist_id":"116","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","date_updated":"2022-03-23T13:08:27Z","type":"journal_article","acknowledgement":"We thank David Dill, Zohar Manna, and Amir Pnueli for helpful discussion.","extern":"1","_id":"4589","status":"public","article_type":"original","abstract":[{"lang":"eng","text":"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.\r\n\r\nCopyright © 1993 Academic Press. All rights reserved."}],"oa":1,"year":"1993","main_file_link":[{"url":"https://www.sciencedirect.com/science/article/pii/S0890540183710254?via%3Dihub","open_access":"1"}],"page":"35 - 77","day":"01","language":[{"iso":"eng"}],"author":[{"full_name":"Alur, Rajeev","first_name":"Rajeev","last_name":"Alur"},{"full_name":"Henzinger, Thomas A","id":"40876CD8-F248-11E8-B48F-1D18A9856A87","first_name":"Thomas A","orcid":"0000−0002−2985−7724","last_name":"Henzinger"}],"article_processing_charge":"No","citation":{"ieee":"R. Alur and T. A. Henzinger, “Real-time logics: Complexity and expressiveness,” <i>Information and Computation</i>, vol. 104, no. 1. Elsevier, pp. 35–77, 1993.","ama":"Alur R, Henzinger TA. Real-time logics: Complexity and expressiveness. <i>Information and Computation</i>. 1993;104(1):35-77. doi:<a href=\"https://doi.org/10.1006/inco.1993.1025\">10.1006/inco.1993.1025</a>","apa":"Alur, R., &#38; Henzinger, T. A. (1993). Real-time logics: Complexity and expressiveness. <i>Information and Computation</i>. Elsevier. <a href=\"https://doi.org/10.1006/inco.1993.1025\">https://doi.org/10.1006/inco.1993.1025</a>","chicago":"Alur, Rajeev, and Thomas A Henzinger. “Real-Time Logics: Complexity and Expressiveness.” <i>Information and Computation</i>. Elsevier, 1993. <a href=\"https://doi.org/10.1006/inco.1993.1025\">https://doi.org/10.1006/inco.1993.1025</a>.","short":"R. Alur, T.A. Henzinger, Information and Computation 104 (1993) 35–77.","mla":"Alur, Rajeev, and Thomas A. Henzinger. “Real-Time Logics: Complexity and Expressiveness.” <i>Information and Computation</i>, vol. 104, no. 1, Elsevier, 1993, pp. 35–77, doi:<a href=\"https://doi.org/10.1006/inco.1993.1025\">10.1006/inco.1993.1025</a>.","ista":"Alur R, Henzinger TA. 1993. Real-time logics: Complexity and expressiveness. Information and Computation. 104(1), 35–77."},"intvolume":"       104","title":"Real-time logics: Complexity and expressiveness","publication_identifier":{"eissn":["0890-5401"]},"scopus_import":"1","quality_controlled":"1","date_published":"1993-05-01T00:00:00Z","volume":104}