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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Thomas Brihaye, Morgane Estiévenart, Gilles Geeraerts, Hsi-Ming Ho, Benjamin Monmege, et al.. Real-time Synthesis is Hard!. 14th International Conference on Formal Modeling and Analysis of Timed Systems (FORMATS'16), Aug 2016, Québec City, Canada. pp.105-120, ⟨10.1007/978-3-319-44878-7_7⟩. ⟨hal-01344684⟩

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