Abstract
We study the realizability problem for specifications of reactive systems expressed in real-time linear temporal logics. The logics we consider are subsets of MITL (Metric Interval Temporal Logic), a logic for which the satisfiability and validity problems are decidable, a necessary condition for the realizability problem to be decidable. On the positive side, we show that the realizability of LTL extended with past real-time formulas is decidable in 2EXPTIME, with a matching lower bound. On the negative side, we show that a simple extension of this decidable fragment with future real-time formulas leads to undecidability. In particular, our results imply that the realizability problem is undecidable for ECL (Event Clock Logic), and therefore also for MITL.
Work supported by the projects: (i) Quasimodo: “Quantitative System Properties in Model-Driven-Design of Embedded”, http://www.quasimodo.aau.dk/, (ii) Gasics: “Games for Analysis and Synthesis of Interactive Computational Systems”, http://www.ulb.ac.be/di/gasics/, and (iii) Moves: “Fundamental Issues in Modelling, Verification and Evolution of Software”, http://moves.ulb.ac.be, a PAI program funded by the Federal Belgian Gouvernment.
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Doyen, L., Geeraerts, G., Raskin, JF., Reichert, J. (2009). Realizability of Real-Time Logics. In: Ouaknine, J., Vaandrager, F.W. (eds) Formal Modeling and Analysis of Timed Systems. FORMATS 2009. Lecture Notes in Computer Science, vol 5813. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04368-0_12
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DOI: https://doi.org/10.1007/978-3-642-04368-0_12
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