What’s decidable about parametric timed automata?

Journal of Logical and Algebraic Methods in Programming

Delahaye

Fournier

2020

Self Cite

We propose a new abstract formalism for probabilistic timed systems, Parametric Interval Probabilistic Timed Automata, based on an extension of Parametric Timed Automata and Interval Markov Chains. In this context, we consider the consistency problem that amounts to deciding whether a given specification admits at least one implementation. In the context of Interval Probabilistic Timed Automata (with no timing parameters), we show that this problem is decidable and propose a constructive algorithm for its resolution. We show that the existence of timing parameter valuations ensuring consistency is undecidable in the general context, but still exhibit a syntactic condition on parameters to ensure decidability. We also propose procedures that resolve both the consistency and the consistent reachability problems when the parametric probabilistic zone graph is finite.

“…The result then follows from the decidability of the EF-universality problem for L/U-PTAs proved in [And19].…”

Section: A Decidability Resultsmentioning

confidence: 84%

Section: A Decidability Resultsmentioning

confidence: 99%

Section: A Decidability Resultsmentioning

confidence: 99%

“…Or put differently, do all valuations reach at least one location of G? Recall that EF-universality is decidable for L/U-PTAs as shown in [And19].…”

Section: A Decidability Resultsmentioning

confidence: 99%

See 2 more Smart Citations

Consistency in Parametric Interval Probabilistic Timed Automata

Journal of Logical and Algebraic Methods in Programming

Delahaye

Fournier

2020

Self Cite

“…"): it is "robustly" undecidable in the sense that, even when varying the setting, undecidability is preserved. For example, EF-emptiness is undecidable even for a single bounded parameter [Mil00], even for a single rational-valued or integer-valued parameter [Ben+15], even with only one clock compared to parameters [Mil00], or with strict constraints only [Doy07] (see [And19] for a survey). Decidability can be obtained using two main directions.…”

Section: Introductionmentioning

confidence: 99%

On the Expressive Power of Invariants in Parametric Timed Automata

2019 24th International Conference on Engineering of Complex Computer Systems (ICECCS)

Lime

Ramparison

2019

The verification of systems combining hard timing constraints with concurrency is challenging. This challenge becomes even harder when some timing constants are missing or unknown. Parametric timed formalisms, such as parametric timed automata (PTAs), tackle the synthesis of such timing constants (seen as parameters) for which a property holds. Such formalisms are highly expressive, but also undecidable, and few decidable subclasses were proposed. We propose here a syntactic restriction on PTAs consisting in removing guards (constraints on transitions) to keep only invariants (constraints on locations). While this restriction preserves the expressiveness of PTAs (and therefore their undecidability), an additional restriction on the type of constraints allows to not only prove decidability, but also to perform the exact synthesis of parameter valuations satisfying reachability. This formalism, that seems trivial at first sight as it benefits from the decidability of the reachability problem with a better complexity than Timed Automata (TAs), suffers from the undecidability of the whole TCTL logic that TAs, on the contrary enjoy. We believe our formalism allows for an interesting trade-off between decidability and practical expressiveness and is therefore promising. We show its applicability in a small case study.

TCTL Model Checking Lower/Upper-Bound Parametric Timed Automata Without Invariants

Lecture Notes in Computer Science

Lime

Ramparison

2018

Self Cite

We study timed systems in which some timing features are unknown parameters. First we consider Upper-bound Parametric Timed Automata (U-PTAs), one of the simplest extensions of timed automata with parameters, in which parameters are only used as clock upper bounds in the constraints. Up to now, there have been several decidability results for the existence of parameter values in U-PTAs such that flat TCTL formulas are satisfied. We prove here that this does not extend to the full logic and that only one level of nesting leads to undecidability. This provides, to the best of our knowledge, the first problem that is decidable for Timed Automata with an undecidable parametric emptiness version for U-PTAs. Second we study Lower/Upper-bound Parametric Timed Automata (L/U-PTAs) in which parameters are used either as clock lower bound, or as clock upper bound, but not both. We prove that without invariants, flat TCTL is decidable for L/U-PTAs by resolving the last non investigated liveness properties.