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Language Preservation Problems in Parametric Timed Automata

Étienne André 1, 2, 3, 4 Didier Lime 5 Nicolas Markey 6
3 MOSEL - Proof-oriented development of computer-based systems
LORIA - FM - Department of Formal Methods
4 VERIDIS - Modeling and Verification of Distributed Algorithms and Systems
MPII - Max-Planck-Institut für Informatik, Inria Nancy - Grand Est, LORIA - FM - Department of Formal Methods
6 SUMO - SUpervision of large MOdular and distributed systems
Inria Rennes – Bretagne Atlantique , IRISA-D4 - LANGAGE ET GÉNIE LOGICIEL
Abstract : Parametric timed automata (PTA) are a powerful formalism to model and reason about concurrent systems with some unknown timing delays. In this paper, we address the (untimed) language- and trace-preservation problems: given a reference parameter valuation, does there exist another parameter valuation with the same untimed language, or with the same set of traces? We show that these problems are undecidable both for general PTA and for the restricted class of L/U-PTA, even for integer-valued parameters, or over bounded time. On the other hand, we exhibit decidable subclasses: 1-clock PTA, and 1-parameter deterministic L-PTA and U-PTA. We also consider robust versions of these problems, where we additionally require that the language be preserved for all valuations between the reference valuation and the new valuation.
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Contributor : Étienne André <>
Submitted on : Wednesday, March 4, 2020 - 9:43:17 AM
Last modification on : Monday, May 17, 2021 - 12:00:05 PM


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Étienne André, Didier Lime, Nicolas Markey. Language Preservation Problems in Parametric Timed Automata. Logical Methods in Computer Science, Logical Methods in Computer Science Association, 2020, 16 (1), ⟨10.23638/LMCS-16⟩. ⟨hal-02498022⟩



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