Algebraic Invariants for Linear Hybrid Automata

Authors Rupak Majumdar, Joël Ouaknine, Amaury Pouly , James Worrell

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Rupak Majumdar
  • Max Planck Institute for Software Systems (MPI-SWS), Kaiserslautern, Germany
Joël Ouaknine
  • Max Planck Institute for Informatics, Saarland Informatics Campus, Saarbrücken, Germany
  • Department of Computer Science, Oxford University, UK
Amaury Pouly
  • Université de Paris, IRIF, CNRS, F-75013 Paris, France
James Worrell
  • Department of Computer Science, Oxford University, UK


We thank Khalil Ghorbal for helpful discussions on the subject of this paper.

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Rupak Majumdar, Joël Ouaknine, Amaury Pouly, and James Worrell. Algebraic Invariants for Linear Hybrid Automata. In 31st International Conference on Concurrency Theory (CONCUR 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 171, pp. 32:1-32:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


We exhibit an algorithm to compute the strongest algebraic (or polynomial) invariants that hold at each location of a given guard-free linear hybrid automaton (i.e., a hybrid automaton having only unguarded transitions, all of whose assignments are given by affine expressions, and all of whose continuous dynamics are given by linear differential equations). Our main tool is a control-theoretic result of independent interest: given such a linear hybrid automaton, we show how to discretise the continuous dynamics in such a way that the resulting automaton has precisely the same algebraic invariants.

Subject Classification

ACM Subject Classification
  • Theory of computation → Timed and hybrid models
  • Theory of computation → Models of computation
  • Hybrid automata
  • algebraic invariants


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