Abstract
We continue investigation of languages, accepted by timed automata of Alur and Dill. In [ACM97] timed regular expressions equivalent to timed automata were introduced. Here we introduce quasilinear equations over timed languages with regular coefficients. We prove that the minimal solution of such an equation is regular and give an algorithm to calculate this solution. This result is used to obtain a new proof of Kleene theorem ([ACM97]) for timed automata. Equations over timed languages can be also considered as an alternative way of specifying these languages.
This research was supported in part by the Russian Foundation for Basic Research under the grants 97-01-00692 and 96-15-96048; and by the International Association for the Promotion of Cooperation with Scientists from the Independent States of the Former Soviet Union (INTAS) under the grant 94-697.
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References
Eugene Asarin, Paul Caspi, and Oded Maler. A Kleene theorem for timed automata. In Proc. 12th Annual IEEE Symposium on Logic in Computer Science, pages 160–171, Warsaw, June 1997. IEEE Computer Society.
Rajeev Alur and David L. Dill. A theory of timed automata. Theoretical Computer Science, 126:183–235, 1994.
Janusz A. Brzozowski. A survey of regular expressions and their applications. IRE Trans. on Electronic Computers, EC-11(3):324–335, 1962.
Conrado Daws, Alfredo Olivero, Stavros Tripakis, and Sergio Yovine. The tool KRONOS. In Rajeev Alur, Thomas A. Henzinger, and Eduardo D. Sontag, editors, Hybrid Systems III, Verification and Control, number 1066 in Lecture Notes in Computer Science, pages 208–219. Springer-Verlag, 1996.
S.C. Kleene. Representations of events in nerve nets and finite automata. In R. McNaughton and H. Yamada, editors, Automata Studies, pages 3–42. Princeton University Press, 1956.
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© 1998 Springer-Verlag Berlin Heidelberg
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Asarin, E. (1998). Equations on timed languages. In: Henzinger, T.A., Sastry, S. (eds) Hybrid Systems: Computation and Control. HSCC 1998. Lecture Notes in Computer Science, vol 1386. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-64358-3_28
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DOI: https://doi.org/10.1007/3-540-64358-3_28
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