License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.CONCUR.2018.26
URN: urn:nbn:de:0030-drops-95644
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2018/9564/
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Roohi, Nima ; Prabhakar, Pavithra ; Viswanathan, Mahesh

Relating Syntactic and Semantic Perturbations of Hybrid Automata

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Abstract

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.

BibTeX - Entry

@InProceedings{roohi_et_al:LIPIcs:2018:9564,
  author =	{Nima Roohi and Pavithra Prabhakar and Mahesh Viswanathan},
  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 =	{Sven Schewe and Lijun Zhang},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/9564},
  URN =		{urn:nbn:de:0030-drops-95644},
  doi =		{10.4230/LIPIcs.CONCUR.2018.26},
  annote =	{Keywords: Model Checking, Hybrid Automata, Approximation, Perturbation}
}

Keywords: Model Checking, Hybrid Automata, Approximation, Perturbation
Collection: 29th International Conference on Concurrency Theory (CONCUR 2018)
Issue Date: 2018
Date of publication: 31.08.2018

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