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

André, Étienne; Lime, Didier; Ramparison, Mathias

doi:10.1007/978-3-030-00151-3_3

Cited by 17 publications

(18 citation statements)

References 18 publications

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“…With the notable exception of [JLR15,ALR18], and to some extent of [BLT09] which addresses the existence of cycles, all the works cited above focus on safety properties, through the basic problem of reachability. This is maybe not so surprising given that most results related to this simpler problem are already negative.…”

Section: Decidability Of Ptasmentioning

confidence: 99%

“…On the positive side, exact synthesis algorithms are proposed for reachability properties in L-PTAs and U-PTAs over integer-valued parameters in [BLT09]. On the negative side, it is shown in [ALR18] that the full TCTL-emptiness problem (i. e., the emptiness of the valuation set for which a particular TCTL formula is satisfied on the model) is undecidable even for U-PTAs. IMITATOR [And21] for PTAs, and Roméo [LRST09] for PTPNs.…”

Section: Introductionmentioning

confidence: 99%

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Reachability and liveness in parametric timed automata

André¹,

Lime²,

Roux³

2022

Logical Methods in Computer Science

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We study timed systems in which some timing features are unknown parameters. Parametric timed automata (PTAs) are a classical formalism for such systems but for which most interesting problems are undecidable. Notably, the parametric reachability emptiness problem, i.e., the emptiness of the parameter valuations set allowing to reach some given discrete state, is undecidable. Lower-bound/upper-bound parametric timed automata (L/U-PTAs) achieve decidability for reachability properties by enforcing a separation of parameters used as upper bounds in the automaton constraints, and those used as lower bounds. In this paper, we first study reachability. We exhibit a subclass of PTAs (namely integer-points PTAs) with bounded rational-valued parameters for which the parametric reachability emptiness problem is decidable. Using this class, we present further results improving the boundary between decidability and undecidability for PTAs and their subclasses such as L/U-PTAs. We then study liveness. We prove that: (1) deciding the existence of at least one parameter valuation for which there exists an infinite run in an L/U-PTA is PSpace-complete; (2) the existence of a parameter valuation such that the system has a deadlock is however undecidable; (3) the problem of the existence of a valuation for which a run remains in a given set of locations exhibits a very thin border between decidability and undecidability.

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Section: Decidability Of Ptasmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Reachability and liveness in parametric timed automata

André¹,

Lime²,

Roux³

2022

Logical Methods in Computer Science

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“…Finally, we showed that the emptiness-problem using nested quantifiers (i.e. beyond EF, EG, AF, AG) automatically leads to the undecidability, even for the very restricted class of U-PTAs with a single parameter (that can even be integer-valued) [ALR18]. In other words, the nested TCTL emptiness problem is undecidable for U-PTAs.…”

Section: The Class Of L/u-ptasmentioning

confidence: 96%

Parametric Verification: An Introduction

André,

Knapik,

Lime

et al. 2019

Preprint

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This paper constitutes a short introduction to parametric verification of concurrent systems. It originates from two 1-day tutorial sessions held at the Petri nets conferences in Toruń (2016) and Zaragoza (2017). A video of the presentation is available at youtube.com/playlist?list=PL9SOLKoGjbeqNcdQVqFpUz7HYqD1fbFIg, consisting of 14 short sequences. The paper presents not only the basic formal concepts tackled in the video version, but also an extensive literature to provide the reader with further references covering the area. We first introduce motivation behind parametric verification in general, and then focus on different models and approaches, for verifying several kinds of systems. They include Parametric Timed Automata, for modelling real-time systems, where the timing constraints are not necessarily known a priori. Similarly, Parametric Interval Markov Chains allow for modelling systems where probabilities of events occurrences are intervals with parametric bounds. Parametric Petri Nets allow for compact representation of systems, and cope with different types of parameters. Finally, Action Synthesis aims at enabling or disabling actions in a concurrent system to guarantee some of its properties. Some tools implementing these approaches were used during hands-on sessions at the tutorial. The corresponding practicals are freely available on the Web.

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“…We exhibit in this section a nested TCTL formula (by opposition to flat TCTL formula, e. g., EF or AF), namely EGAF =0 ap for some atomic property ap and prove that EGAF =0 -emptiness is undecidable for (possibly bounded) PTA U I . The formula EGAF =0 was already used to prove the TCTL-emptiness of U-PTAs in [ALR18]. This implies the undecidability of the whole TCTL-emptiness problem for (possibly bounded) PTA U I .…”

Section: B Undecidability Of Tctl-emptinessmentioning

confidence: 99%

On the Expressive Power of Invariants in Parametric Timed Automata

André

Lime

Ramparison

2019

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

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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.

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

Cited by 17 publications

References 18 publications

Reachability and liveness in parametric timed automata

Reachability and liveness in parametric timed automata

Parametric Verification: An Introduction

On the Expressive Power of Invariants in Parametric Timed Automata

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