A computable and compositional semantics for hybrid automata

Davide Bresolin*, Pieter Collins, Luca Geretti, Roberto Segala, Tiziano Villa, Sanja Zivanovic Gonzalez

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference article in proceedingAcademicpeer-review

64 Downloads (Pure)


Hybrid Systems are systems having a mixed discrete and continuous behaviour that cannot be characterized faithfully using either only discrete or only continuous models. A good framework for hybrid systems should support their compositional description and analysis, since commonly systems are specified by a composition of smaller subsystems, to cope with the complexity of their monolithic representation. Moreover, since the reachability problem for hybrid systems is undecidable, one should investigate the conditions that guarantee approximate computability of composition, when only approximations to the exact problem data are available.

In this paper, we propose an automata-based formalism (HIOA) for hybrid systems that is compositional and for which the evolution can be computed approximately. The main results are that the composition of compatible HIOA yields a pre-HIOA; a dominance result on the composition of HIOA by which we can replace any component in a composition by another one that exhibits the same external behaviour without affecting the behaviour of the composition; finally, the key result that the composition of two compatible upper(lower)-semicontinuous HIOA is a computable upper(lower)-semicontinuous pre-HIOA, which entails that the evolution of the composition is upper(lower)-semicomputable. A discussion on how compositionality/computability are handled in state-of-art libraries for reachability analysis closes the paper.

Original languageEnglish
Title of host publicationHSCC '20: Proceedings of the 23rd International Conference on Hybrid Systems: Computation and Control
Place of PublicationNew York
PublisherThe Association for Computing Machinery
Number of pages11
ISBN (Print)978-1-4503-7018-9
Publication statusPublished - 2020
Event23rd International Conference on Hybrid Systems: Computation and ControlComputation and Control - Sydney, Australia
Duration: 21 Apr 202024 Apr 2020


Conference23rd International Conference on Hybrid Systems
Abbreviated titleHSCC 2020


  • Composition
  • Computability
  • Hybrid Automata

Cite this