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Relating Syntactic and Semantic Perturbations of Hybrid Automata

Authors: Nima Roohi, Pavithra Prabhakar, and Mahesh Viswanathan

Published in: LIPIcs, Volume 118, 29th International Conference on Concurrency Theory (CONCUR 2018)

We investigate how the semantics of a hybrid automaton deviates with respect to syntactic perturbations on the hybrid automaton. We consider syntactic perturbations of a hybrid automaton, wherein the syntactic representations of its elements, namely, initial sets, invariants, guards, and flows, in some logic are perturbed. Our main result establishes a continuity like property that states that small perturbations in the syntax lead to small perturbations in the semantics. More precisely, we show that for every real number epsilon>0 and natural number k, there is a real number delta>0 such that H^delta, the delta syntactic perturbation of a hybrid automaton H, is epsilon-simulation equivalent to H up to k transition steps. As a byproduct, we obtain a proof that a bounded safety verification tool such as dReach will eventually prove the safety of a safe hybrid automaton design (when only non-strict inequalities are used in all constraints) if dReach iteratively reduces the syntactic parameter delta that is used in checking approximate satisfiability. This has an immediate application in counter-example validation in a CEGAR framework, namely, when a counter-example is spurious, then we have a complete procedure for deducing the same.

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Nima Roohi, Pavithra Prabhakar, and Mahesh Viswanathan. Relating Syntactic and Semantic Perturbations of Hybrid Automata. In 29th International Conference on Concurrency Theory (CONCUR 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 118, pp. 26:1-26:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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  author =	{Roohi, Nima and Prabhakar, Pavithra and Viswanathan, Mahesh},
  title =	{{Relating Syntactic and Semantic Perturbations of Hybrid Automata}},
  booktitle =	{29th International Conference on Concurrency Theory (CONCUR 2018)},
  pages =	{26:1--26:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-087-3},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{118},
  editor =	{Schewe, Sven and Zhang, Lijun},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2018.26},
  URN =		{urn:nbn:de:0030-drops-95644},
  doi =		{10.4230/LIPIcs.CONCUR.2018.26},
  annote =	{Keywords: Model Checking, Hybrid Automata, Approximation, Perturbation}
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