# A determinizable class of timed automata

## Abstract

We introduce the class of *event- recording timed automata* (ERA). An event-recording automaton contains, for every event *a*, a clock that records the time of the last occurrence of *a.* The class ERA is, on one hand, expressive enough to model (finite) timed transition systems and, on the other hand, determinizable and closed under all boolean operations. As a result, the language inclusion problem is decidable for event-recording automata. We present a translation from timed transition systems to event-recording automata, which leads to an algorithm for checking if two timed transition systems have the same set of timed behaviors.

We also consider *event-predicting timed automata* (EPA), which contain clocks that predict the time of the next occurrence of an event. The class of *event-clock automata* (ECA), which contain both event-recording and event-predicting clocks, is a suitable specification language for real-time properties. We provide an algorithm for checking if a timed automaton meets a specification that is given as an event-clock automaton.

## References

- 1.R. Alur, C. Courcoubetis, and D. Dill. Model-checking in dense real-time.
*Information and Computation*, 104:2–34, 1993.CrossRefGoogle Scholar - 2.R. Alur, C. Courcoubetis, and T. Henzinger. Computing accumulated delays in real-time systems. In
*Proceedings of the Fifth Conference on Computer-Aided Verification*, Lecture Notes in Computer Science 697, pages 181–193. Springer-Verlag, 1993.Google Scholar - 3.R. Alur and D. Dill. Automata for modeling real-time systems. In
*Proceedings of the 17th International Colloquium on Automata, Languages, and Programming*, Lecture Notes in Computer Science 443, pages 322–335. Springer-Verlag, 1990.Google Scholar - 4.R. Alur, T. Feder, and T. Henzinger. The benefits of relaxing punctuality. In
*Proceedings of the Tenth ACM Symposium on Principles of Distributed Computing*, pages 139–152, 1991.Google Scholar - 5.R. Alur and T. Henzinger. Back to the future: Towards a theory of timed regular languages. In
*Proceedings of the 33rd IEEE Symposium on Foundations of Computer Science*, pages 177–186, 1992.Google Scholar - 6.C. Courcoubetis and M. Yannakakis. Minimum and maximum delay problems in real-time systems. In
*Proceedings of the Third Workshop on Computer-Aided Verification*, Lecture Notes in Computer Science 575, pages 399–409, 1991.Google Scholar - 7.T. Henzinger, Z. Manna, and A. Pnueli. Temporal proof methodologies for realtime systems. In
*Proceedings of the 18th ACM Symposium on Principles of Programming Languages*, pages 353–366, 1991.Google Scholar - 8.T. Henzinger, X. Nicollin, J. Sifakis, and S. Yovine. Symbolic model-checking for real-time systems. In
*Proceedings of the Seventh IEEE Symposium on Logic in Computer Science*, pages 394–406, 1992.Google Scholar - 9.J. Hopcroft and J. Ullman.
*Introduction to Automata Theory, Languages, and Computation*. Addison-Wesley, 1979.Google Scholar - 10.R. Kurshan. Reducibility in analysis of coordination. In
*Lecture Notes in Computer Science*, volume 103, pages 19–39. Springer-Verlag, 1987.Google Scholar - 11.N. Lynch and H. Attiya. Using mappings to prove timing properties.
*Distributed Computing*, 6:121–139, 1992.Google Scholar - 12.Z. Manna and A. Pnueli.
*The Temporal Logic of Reactive and Concurrent Systems*. Springer-Verlag, 1991.Google Scholar - 13.M. Merritt, F. Modugno, and M. Tuttle. Time-constrained automata. In
*Proceedings of the Workshop on Theories of Concurrency*, Lecture Notes in Computer Science 527, pages 408–423. Springer-Verlag, 1991.Google Scholar - 14.F. Schneider, B. Bloom, and K. Marzullo. Putting time into proof outlines. In
*Real-Time: Theory in Practice*, Lecture Notes in Computer Science 600, pages 618–639. Springer-Verlag, 1991.Google Scholar - 15.A. Sistla, M. Vardi, and P. Wolper. The complementation problem for Büchi automata with applications to temporal logic.
*Theoretical Computer Science*, 49:217–237, 1987.CrossRefGoogle Scholar - 16.P. Wolper, M. Vardi, and A. Sistla. Reasoning about infinite computation paths. In
*Proceedings of the 24th IEEE Symposium on Foundations of Computer Science*, pages 185–194, 1983.Google Scholar - 17.T. Yoneda, A. Shibayam, B. Schlingloff, and E. Clarke. Efficient verification of parallel real-time systems. In
*Proceedings of the Fifth Conference on Computer-Aided Verification*, Lecture Notes in Computer Science 697, pages 321–332. Springer-Verlag, 1993.Google Scholar