Logical Characterisation of Hybrid Conformance

Authors Maciej Gazda, Mohammad Reza Mousavi

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Maciej Gazda
  • Department of Computer Science, University of Sheffield, UK
Mohammad Reza Mousavi
  • School of Informatics, University of Leicester, UK


We thank Rayna Dimitrova for her helpful comments on an earlier version of this article. We also thank anonymous ICALP reviewers for their thorough feedback which helped us improve the paper.

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Maciej Gazda and Mohammad Reza Mousavi. Logical Characterisation of Hybrid Conformance. In 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 168, pp. 130:1-130:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


Logical characterisation of a behavioural equivalence relation precisely specifies the set of formulae that are preserved and reflected by the relation. Such characterisations have been studied extensively for exact semantics on discrete models such as bisimulations for labelled transition systems and Kripke structures, but to a much lesser extent for approximate relations, in particular in the context of hybrid systems. We present what is to our knowledge the first characterisation result for approximate notions of hybrid refinement and hybrid conformance involving tolerance thresholds in both time and value. Since the notion of conformance in this setting is approximate, any characterisation will unavoidably involve a notion of relaxation, denoting how the specification formulae should be relaxed in order to hold for the implementation. We also show that an existing relaxation scheme on Metric Temporal Logic used for preservation results in this setting is not tight enough for providing a characterisation of neither hybrid conformance nor refinement. The characterisation result, while interesting in its own right, paves the way to more applied research, as our notion of hybrid conformance underlies a formal model-based technique for the verification of cyber-physical systems.

Subject Classification

ACM Subject Classification
  • Theory of computation → Logic and verification
  • Software and its engineering → Formal software verification
  • Logical Characterisation
  • Metric Temporal Logic
  • Conformance
  • Behavioural Equivalence
  • Hybrid Systems
  • Relaxation


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