Relating syntactic and semantic perturbations of hybrid automata

Nima Roohi, Pavithra Prabhakar, Mahesh Viswanathan

Research output: Chapter in Book/Report/Conference proceedingConference contribution


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 > 0 and natural number k, there is a real number δ > 0 such that Hδ, the δ syntactic perturbation of a hybrid automaton H, is -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 δ 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.

Original languageEnglish (US)
Title of host publication29th International Conference on Concurrency Theory, CONCUR 2018
EditorsSven Schewe, Lijun Zhang
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Print)9783959770873
StatePublished - Aug 1 2018
Event29th International Conference on Concurrency Theory, CONCUR 2018 - Beijing, China
Duration: Sep 4 2018Sep 7 2018

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
ISSN (Print)1868-8969


Other29th International Conference on Concurrency Theory, CONCUR 2018


  • Approximation
  • Hybrid automata
  • Perturbation
  • Phrases model checking

ASJC Scopus subject areas

  • Software


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