A New Modality for Almost Everywhere Properties in Timed Automata
The context of this study is timed temporal logics for timed automata. In this paper, we propose an extension of the classical logic TCTL with a new Until modality, called “Until almost everywhere”. In the extended logic, it is possible, for instance, to express that a property is true at all positions of all runs, except on a negligible set of positions. Such properties are very convenient, for example in the framework of boolean program verification, where transitions result from changing variable values. We investigate the expressive power of this modality and in particular, we prove that it cannot be expressed with classical TCTL modalities. However, we show that model-checking the extended logic remains PSPACE-complete as for TCTL.
KeywordsAction Transition Temporal Logic Atomic Proposition Extended Logic Linear Time Temporal Logic
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- [AH92]Alur, R., Henzinger, T.A.: Logics and models of real-time: a survey. In: de Bakker, J.W., de Roever, W.-P., Rozenberg, G. (eds.) REX 1992. LNCS, vol. 666, pp. 74–106. Springer, Heidelberg (1993)Google Scholar
- [BMBBL05]Bel Mokadem, H., Bérard, B., Bouyer, P., Laroussinie, F.: A new modality for almost everywhere properties in timed automata. Research Report LSV-05-06, LSV, ENS de Cachan, France (2005) Google Scholar
- [Eme91]Emerson, E.A.: Temporal and Modal Logic. (Formal Models and Semantics) Handbook of Theoretical Computer Science, vol. B, pp. 995–1072. MIT Press, Cambridge (1991)Google Scholar
- [IEC93]IEC (International Electrotechnical Commission). IEC Standard 61131-3: Programmable controllers - Part 3 (1993) Google Scholar
- [LLW95]Laroussinie, F., Larsen, K.G., Weise, C.: From timed automata to logic – and back. In: Hájek, P., Wiedermann, J. (eds.) MFCS 1995. LNCS, vol. 969, pp. 529–539. Springer, Heidelberg (1995)Google Scholar