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Verifying Stochastic Hybrid Systems with Temporal Logic Specifications via Model Reduction

Published:15 November 2021Publication History
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Abstract

We present a scalable methodology to verify stochastic hybrid systems for inequality linear temporal logic (iLTL) or inequality metric interval temporal logic (iMITL). Using the Mori–Zwanzig reduction method, we construct a finite-state Markov chain reduction of a given stochastic hybrid system and prove that this reduced Markov chain is approximately equivalent to the original system in a distributional sense. Approximate equivalence of the stochastic hybrid system and its Markov chain reduction means that analyzing the Markov chain with respect to a suitably strengthened property allows us to conclude whether the original stochastic hybrid system meets its temporal logic specifications. Based on this, we propose the first statistical model checking algorithms to verify stochastic hybrid systems against correctness properties, expressed in iLTL or iMITL. The scalability of the proposed algorithms is demonstrated by a case study.

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          cover image ACM Transactions on Embedded Computing Systems
          ACM Transactions on Embedded Computing Systems  Volume 20, Issue 6
          November 2021
          256 pages
          ISSN:1539-9087
          EISSN:1558-3465
          DOI:10.1145/3485150
          • Editor:
          • Tulika Mitra
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          Publication History

          • Published: 15 November 2021
          • Accepted: 1 August 2021
          • Revised: 1 June 2021
          • Received: 1 September 2020
          Published in tecs Volume 20, Issue 6

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