Reachability Problems and Abstract State Spaces for Time Petri Nets with Stopwatches

Berthomieu, Bernard; Lime, Didier; Roux, Olivier H.; Vernadat, François

doi:10.1007/s10626-006-0011-y

Cited by 56 publications

(66 citation statements)

References 14 publications

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“…and [a 4 , b 4 ] = [3,11] . Let us consider the following simulation for k = 0, 1 and 2. k 0 1 2 x 1 4 11 11 x 2 0 7 14 x 3 0 6 13 The first table contains the firing dates while each column k of the second table is the bounds of the sojourn time (in absolute time) of the tokens, produced by the k th firing of the transitions x 1 , x 2 and x 3 in each place.…”

Section: (Max +) Model Of P-time Event Graphsmentioning

confidence: 99%

“…In this paper, these assumptions are not taken as the considered models are nonbounded Event Graphs where the values of the temporisations are defined in R + . Contrary to the polyhedra of the classes which generally are approximations of the possible dates [3], the spaces considered in this paper are exact because the concept of lattice is relevant in the event graphs.…”

Section: Introductionmentioning

confidence: 99%

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From Extremal Trajectories to Token Deaths in P-time Event Graphs

Declerck

2011

IEEE Trans. Automat. Contr.

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Abstract-In this paper, we consider the (max, +) model of P-time Event Graphs whose behaviors are defined by lower and upper bound constraints. The extremal trajectories of the system starting from an initial interval are characterized with a particular series of matrices for a given finite horizon. Two dual polynomial algorithms are proposed to check the existence of feasible trajectories. The series of matrices are used in the determination of the maximal horizon of consistency and the calculation of the date of the first token deaths.

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Section: (Max +) Model Of P-time Event Graphsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

From Extremal Trajectories to Token Deaths in P-time Event Graphs

Declerck

2011

IEEE Trans. Automat. Contr.

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“…For these three models, reachability is undecidable even when the net is bounded (i.e., there exists a constant k such that for all reachable states, the number of tokens in any place is less than k) (Berthomieu et al 2007). Reachability and related results are then obtained by computing the state-space if it is computable.…”

Section: Formal Models For Online Schedulingmentioning

confidence: 99%

Formal verification of real-time systems with preemptive scheduling

Lime¹,

Roux²

2008

Real-Time Syst

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Abstract. In this paper, we propose a method for the verification of timed properties for real-time systems featuring a preemptive scheduling policy: the system, modeled as a scheduling time Petri net, is first translated into a linear hybrid automaton to which it is time-bisimilar. Timed properties can then be verified using HyTech. The efficiency of this approach leans on two major points: first, the translation features a minimization of the number of variables (clocks) of the resulting automaton, which is a critical parameter for the efficiency of the ensuing verification. Second, the translation is performed by an over-approximating algorithm, which is based on Difference Bound Matrix and therefore efficient, that nonetheless produces a time-bisimilar automaton despite the over-approximation. The proposed modeling and verification method are generic enough to account for many scheduling policies. In this paper, we specifically show how to deal with Fixed Priority and Earliest Deadline First policies, with the possibility of using Round-Robin for tasks with the same priority. We have implemented the method and give some experimental results illustrating its efficiency.

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“…Several extensions of time Petri nets have been proposed to express the preemptive scheduling of tasks, such as Scheduling-TPNs [2], inhibitor hyperarc TPNs (ITPNs) [3] or Preemptive-TPNs [4]. All these models belong to the class of TPNs extended with stopwatches (SwPNs) [5]. Reachability and most other properties of interest are however undecidable for SwPNs, even when bounded [5].…”

Section: Introductionmentioning

confidence: 99%

“…All these models belong to the class of TPNs extended with stopwatches (SwPNs) [5]. Reachability and most other properties of interest are however undecidable for SwPNs, even when bounded [5].…”

Section: Introductionmentioning

confidence: 99%

Romeo: A Parametric Model-Checker for Petri Nets with Stopwatches

Lime

Roux

Seidner

et al. 2009

Lecture Notes in Computer Science

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Abstract. Last time we reported on Romeo, analyses with this tool were mostly based on translations to other tools. This new version provides an integrated TCTL model-checker and has gained in expressivity with the addition of parameters. Although there exists other tools to compute the state-space of stopwatch models, Romeo is the first one that performs TCTL model-checking on stopwatch models. Moreover, it is the first tool that performs TCTL model-checking on timed parametric models. Indeed, Romeo now features an efficient model-checking of time Petri nets using the Uppaal DBM Library, the model-checking of stopwatch Petri nets and parametric stopwatch Petri nets using the Parma Polyhedra Library and a graphical editor and simulator of these models. Furthermore, its audience has increased leading to several industrial contracts. This paper reports on these recent developments of Romeo.

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Reachability Problems and Abstract State Spaces for Time Petri Nets with Stopwatches

Cited by 56 publications

References 14 publications

From Extremal Trajectories to Token Deaths in P-time Event Graphs

From Extremal Trajectories to Token Deaths in P-time Event Graphs

Formal verification of real-time systems with preemptive scheduling

Romeo: A Parametric Model-Checker for Petri Nets with Stopwatches

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