eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2018-08-31
26:1
26:16
10.4230/LIPIcs.CONCUR.2018.26
article
Relating Syntactic and Semantic Perturbations of Hybrid Automata
Roohi, Nima
1
Prabhakar, Pavithra
2
Viswanathan, Mahesh
3
Univeristy of Pennsylvania, USA
Kansas State University, USA, http://people.cs.ksu.edu/~pprabhakar/
University of Illinois at Urbana-Champaign, USA, http://vmahesh.cs.illinois.edu/
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol118-concur2018/LIPIcs.CONCUR.2018.26/LIPIcs.CONCUR.2018.26.pdf
Model Checking
Hybrid Automata
Approximation
Perturbation