Abstract
We consider a general notion of timed automata with input-determined guards and show that they admit a robust logical framework along the lines of [6], in terms of a monadic second order logic characterisation and an expressively complete timed temporal logic. We then generalize these automata using the notion of recursive operators introduced by Henzinger, Raskin, and Schobbens [10], and show that they admit a similar logical framework. These results hold in the “pointwise” semantics. We finally use this framework to show that the real-time logic MITL of Alur et al [2] is expressively complete with respect to an MSO corresponding to an appropriate set of input-determined operators.
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References
Alur, R., Dill, D.L.: A theory of timed automata. Theoretical Computer Science 126, 183–235 (1994)
Alur, R., Feder, T., Henzinger, T.A.: The benefits of relaxing punctuality. J. ACM 43, 116–146 (1996)
Alur, R., Fix, L., Henzinger, T.A.: Event-clock automata: a determinizable class of timed automata. In: Dill, D.L. (ed.) CAV 1994. LNCS, vol. 818, pp. 1–13. Springer, Heidelberg (1994)
Alur, R., Henzinger, T.A.: Real-time logics: complexity and expressiveness. Information and Computation 104, 35–77 (1993)
Büchi, J.R.: Weak second-order arithmetic and finite automata, Zeitschrift für Math. Logik und Grundlagen der Mathematik 6, 66–92 (1960)
D’Souza, D.: A Logical Characterisation of Event Clock Automata. J. Foundations of Computer Science 14(4), World Scientific (2003)
D’Souza, D., Tabareau, N.: On timed automata with input-determined guards, Technical report TR-2004-1, CSA/IISc, http://archive.csa.iisc.ernet.in/TR
D’Souza, D., Thiagarajan, P.S.: Product Interval Automata: A Subclass of Timed Automata. In: Matsuoka, S., Tholburn, M. (eds.) ISCOPE 1999. LNCS, vol. 1732, Springer, Heidelberg (1999)
Gabbay, D., Pnueli, A., Shelah, S., Stavi, J.: The Temporal Analysis of Fairness. In: Seventh ACM Symposium on Principles of Programming Languages, pp. 163–173 (1980)
Henzinger, T.A., Raskin, J.-F., Schobbens, P.-Y.: The regular real-time languages. In: Larsen, K.G., Skyum, S., Winskel, G. (eds.) ICALP 1998. LNCS, vol. 1443, pp. 580–591. Springer, Heidelberg (1998)
Kamp, H.: Tense Logic and the Theory of Linear Order, PhD Thesis, University of California (1968)
Koymans, R.: Specifying real-time properties with metric temporal logic. Real-time Systems 2(4), 255–299 (1990)
Pnueli, A.: The temporal logic of programs. In: Proc. 18th IEEE FOCS, pp. 46–57 (1977)
Raskin, J.-F.: Logics, Automata and Classical Theories for Deciding Real Time, Ph.D Thesis, FUNDP, Belgium (1999)
Raskin, J.-F., Schobbens, P.-Y.: State-clock Logic: A Decidable Real-Time Logic. In: Maler, O. (ed.) HART 1997. LNCS, vol. 1201, pp. 33–47. Springer, Heidelberg (1997)
Thomas, W.: Automata on Infinite Objects. In: Leeuwen, J.V. (ed.) Handbook of Theoretical Computer Science, vol. B, pp. 133–191. Elsevier, Amsterdam (1990)
Wilke, T.: Specifying Timed State Sequences in Powerful Decidable Logics and Timed Automata. In: Langmaack, H., de Roever, W.-P., Vytopil, J. (eds.) FTRTFT 1994 and ProCoS 1994. LNCS, vol. 863, pp. 694–715. Springer, Heidelberg (1994)
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D’Souza, D., Tabareau, N. (2004). On Timed Automata with Input-Determined Guards. In: Lakhnech, Y., Yovine, S. (eds) Formal Techniques, Modelling and Analysis of Timed and Fault-Tolerant Systems. FTRTFT FORMATS 2004 2004. Lecture Notes in Computer Science, vol 3253. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30206-3_7
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DOI: https://doi.org/10.1007/978-3-540-30206-3_7
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