Real-time Synthesis is Hard!

Abstract : We study the reactive synthesis problem (RS) for specifications given in Metric Interval Temporal Logic (MITL). RS is known to be undecidable in a very general setting, but on infinite words only; and only the very restrictive BResRS subcase is known to be decidable (see D'Souza et al. and Bouyer et al.). In this paper, we precise the decidabil-ity border of MITL synthesis. We show RS is undecidable on finite words too, and present a landscape of restrictions (both on the logic and on the possible controllers) that are still undecidable. On the positive side, we revisit BResRS and introduce an efficient on-the-fly algorithm to solve it.
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Martin Fränzle; Nicolas Markey. 14th International Conference on Formal Modeling and Analysis of Timed Systems (FORMATS'16), Aug 2016, Québec City, Canada. Springer, Proceedings of the 14th International Conference on Formal Modeling and Analysis of Timed Systems (FORMATS'16), 9884, pp.105-120, 2016, Lecture Notes in Computer Science. 〈10.1007/978-3-319-44878-7_7〉
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Thomas Brihaye, Morgane Estiévenart, Gilles Geeraerts, Hsi-Ming Ho, Benjamin Monmege, et al.. Real-time Synthesis is Hard!. Martin Fränzle; Nicolas Markey. 14th International Conference on Formal Modeling and Analysis of Timed Systems (FORMATS'16), Aug 2016, Québec City, Canada. Springer, Proceedings of the 14th International Conference on Formal Modeling and Analysis of Timed Systems (FORMATS'16), 9884, pp.105-120, 2016, Lecture Notes in Computer Science. 〈10.1007/978-3-319-44878-7_7〉. 〈hal-01344684〉

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