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Discrete Semantics for Hybrid Automata

Avoiding Misleading Assumptions in Systems Biology

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Abstract

Many natural systems exhibit a hybrid behavior characterized by a set of continuous laws which are switched by discrete events. Such behaviors can be described in a very natural way by a class of automata called hybrid automata. Their evolution are represented by both dynamical systems on dense domains and discrete transitions. Once a real system is modeled in a such framework, one may want to analyze it by applying automatic techniques, such as Model Checking or Abstract Interpretation. Unfortunately, the discrete/continuous evolutions not only provide hybrid automata of great flexibility, but they are also at the root of many undecidability phenomena. This paper addresses issues regarding the decidability of the reachability problem for hybrid automata (i.e., “can the system reach a state a from a state b?”) by proposing an “inaccurate” semantics. In particular, after observing that dense sets are often abstractions of real world domains, we suggest, especially in the context of biological simulation, to avoid the ability of distinguishing between values whose distance is less than a fixed ε. On the ground of the above considerations, we propose a new semantics for first-order formulæ which guarantees the decidability of reachability. We conclude providing a paradigmatic biological example showing that the new semantics mimics the real world behavior better than the precise one.

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Acknowledgements

The authors thank T. Colcombet, A. Montanari, and G. Puppis for useful discussions.

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Authors and Affiliations

  1. DMI, Univ. di Trieste, Via Valerio, 12/1, 34127, Trieste, Italy

    Alberto Casagrande

  2. Applied Genomics Institute, Via Linussio, 51, 33100, Udine, Italy

    Alberto Casagrande & Alberto Policriti

  3. DIMI, Univ. di Udine, Via delle Scienze, 206, 33100, Udine, Italy

    Carla Piazza & Alberto Policriti

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  1. Alberto Casagrande
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  2. Carla Piazza
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  3. Alberto Policriti
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Correspondence to Alberto Casagrande.

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This work has been partially supported by regional project BioCheck.

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Casagrande, A., Piazza, C. & Policriti, A. Discrete Semantics for Hybrid Automata. Discrete Event Dyn Syst 19, 471–493 (2009). https://doi.org/10.1007/s10626-009-0082-7

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