A Forward Reachability Algorithm for Bounded Timed-Arc Petri Nets

David, Albert; Jacobsen, Lasse; Jacobsen, Morten; Srba, Jǐŕı

doi:10.4204/eptcs.102.12

Cited by 5 publications

(2 citation statements)

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“…For TPNs, this corresponds to the weak semantics [24], under which the reachable (untimed) markings are the markings reachable by the associated (untimed) Petri net. The second approach considers only bounded nets [15] (see also bounded TPNs [7]). Our goal in this paper is to define restrictions for Timed-Arc PNU that ensure decidability for models combining urgency and unbounded nets.…”

Section: Undecidable and Decidable Problems For Timed-arc Pnumentioning

confidence: 99%

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Decidable Classes of Unbounded Petri Nets with Time and Urgency

Akshay¹,

Genest²,

Hélouët³

2016

Application and Theory of Petri Nets and Concurrency

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Abstract. Adding real time information to Petri net models often leads to undecidability of classical verification problems such as reachability and boundedness. For instance, models such as Timed-Transition Petri nets (TPNs) [22] are intractable except in a bounded setting. On the other hand, the model of TimedArc Petri nets [26] enjoys decidability results for boundedness and control-state reachability problems at the cost of disallowing urgency (the ability to enforce actions within a time delay). Our goal is to investigate decidable classes of Petri nets with time that capture some urgency and still allow unbounded behaviors, which go beyond finite state systems. We present, up to our knowledge, the first decidability results on reachability and boundedness for Petri net variants that combine unbounded places, time, and urgency. For this, we introduce the class of Timed-Arc Petri nets with restricted Urgency, where urgency can be used only on transitions consuming tokens from bounded places. We show that control-state reachability and boundedness are decidable for this new class, by extending results from Timed-Arc Petri nets (without urgency) [2]. Our main result concerns (marking) reachability, which is undecidable for both TPNs (because of unrestricted urgency) [20] and Timed-Arc Petri Nets (because of infinite number of "clocks") [25]. We obtain decidability of reachability for unbounded TPNs with restricted urgency under a new, yet natural, timed-arc semantics presenting them as Timed-Arc Petri Nets with restricted urgency. Decidability of reachability under the intermediate marking semantics is also obtained for a restricted subclass.

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Section: Undecidable and Decidable Problems For Timed-arc Pnumentioning

confidence: 99%

“…In earlier works, decidability results have been obtained by either imposing a bound on the number of tokens (e.g., [15,7]) or removing urgency completely (e.g., [21,24]). Here, we consider classes of Timed-Arc Petri Nets and of TPNs with restricted Urgency to obtain decidability.…”

Section: Introductionmentioning

confidence: 99%

Decidable Classes of Unbounded Petri Nets with Time and Urgency

Akshay¹,

Genest²,

Hélouët³

2016

Application and Theory of Petri Nets and Concurrency

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Interval Abstraction Refinement for Model Checking of Timed-Arc Petri Nets

Birch

Jacobsen

Jensen

et al. 2014

Lecture Notes in Computer Science

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Abstract. State-space explosion is a major obstacle in verification of time-critical distributed systems. An important factor with a negative influence on the tractability of the analysis is the size of constants that clocks are compared to. This problem is particularly accented in explicit state-space exploration techniques. We suggest an approximation method for reducing the size of constants present in the model. The proposed method is developed for Timed-Arc Petri Nets and creates an under-approximation or an over-approximation of the model behaviour. The verification of approximated Petri net models can be considerably faster but it does not in general guarantee conclusive answers. We implement the algorithms within the open-source model checker TAPAAL and demonstrate on a number of experiments that our approximation techniques often result in a significant speed-up of the verification.

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