A Trace Semantics for Petri Nets

Hoogers, P. W.; Kleijn, H. C. M.; Thiagarajan, P. S.

doi:10.1006/inco.1995.1032

Cited by 41 publications

(13 citation statements)

References 20 publications

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“…Adjacency is similar to the idea of Mazurkiewicz traces [12], allowing to exchange concurrent transitions. However, it is based on the semantic notion of concurrency instead of the global syntactic independence relation in trace theory, similar as in the approach of generalising trace theory in [10]. Note that ↔ * -related firing sequences contain the same (finite) multiset of transition occurrences.…”

Section: Abstract Runs Of Place/transition Systemsmentioning

confidence: 97%

“…In this paper we continue the line of research of [6,13,3,11,10] to formalise a causality-based notion of run of a Petri net that fits the collective token interpretation. As remarked already in [6], what we need is some notion of an "abstract process" and a notion of maximality for abstract processes, such that a P/T-system is conflict-free iff it has exactly one maximal abstract process starting at the initial marking.…”

Section: Introductionmentioning

confidence: 98%

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Abstract processes of place/transition systems

Glabbeek

Goltz

Schicke

2011

Information Processing Letters

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A well-known problem in Petri net theory is to formalise an appropriate causality-based concept of process or run for place/transition systems. The so-called individual token interpretation, where tokens are distinguished according to their causal history, giving rise to the processes of Goltz and Reisig, is often considered too detailed. The problem of defining a fully satisfying more abstract concept of process for general place/transition systems has so-far not been solved. In this paper, we recall the proposal of defining an abstract notion of process, here called BD-process, in terms of equivalence classes of GoltzReisig processes, using an equivalence proposed by Best and Devillers. It yields a fully satisfying solution for at least all one-safe nets. However, for certain nets which intuitively have different conflicting behaviours, it yields only one maximal abstract process. Here we identify a class of place/transition systems, called structural conflict nets, where conflict and concurrency due to token multiplicity are clearly separated. We show that, in the case of structural conflict nets, the equivalence proposed by Best and Devillers yields a unique maximal abstract process only for conflict-free nets. Thereby BD-processes constitute a simple and fully satisfying solution in the class of structural conflict nets.

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Section: Abstract Runs Of Place/transition Systemsmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 98%

Abstract processes of place/transition systems

Glabbeek

Goltz

Schicke

2011

Information Processing Letters

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“…In particular, we are interested in the step property of step transition systems [13] and their relationship to Mazurkiewicz trace languages [7] and, more precisely, generalized trace languages [6]. Definition 1: (Adapted from [13]) A deterministic transition system (Q, q 0 , δ) satisfies the step property if it ensures that transitions with non-atomic labels can be decomposed into arbitrary sequences of decompositions of the label.…”

Section: A Finite Mind-the-gap Automatonmentioning

confidence: 99%

“…The language of a transition system with the step property is a generalized trace language [6], generalizing Mazurkiewicz trace languages [7], and defined as follows.…”

Section: A Finite Mind-the-gap Automatonmentioning

confidence: 99%

Mind the gap: Expanding communication options in decentralized discrete-event control

Ricker

Caillaud

2007

2007 46th IEEE Conference on Decision and Control

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Frameworks that incorporate communication into decentralized supervisory control theory address the following problem: find locations in the evolution of the plant behavior where some supervisors send information so that a supervisor that was unable to make the correct control decision prior to receiving external information, is now capable of making the correct control decision. Proposed solutions to this problem identify an earliest and a latest placement where such communication results in the synthesis of a correct control solution.In addition to a first and last communication opportunity, there may be a selection of intermediate possibilities where communication would produce the correct control solution. We present a computable procedure to identify a broader range of suitable communication locations.

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“…Regions were introduced in the seminal paper [17] for the class of Elementary Net Systems (en-systems) with sequential execution semantics. After that, the original idea has been developed (see, for example, [27]) and extended in several different directions, including: other Petri net classes (e.g., bounded pt-nets without loops [6], pt-nets [26], Flip-flop nets [29], nets with inhibitor arcs [8,28], and nets with localities [25]); synthesis modules of implemented tool frameworks (e.g., Petrify [12], ProM [31], VipTool [5], Genet [9], and Rbminer [30]); application areas (e.g., asynchronous VLSI circuits [12,9,30] and workflows [31]); other semantical execution models (e.g., step sequences [19,28], (local) maximal concurrency [25], and firing policies [14]); and specification formalisms other than transition systems (e.g., languages [13] and scenarios [5]). More details concerning the importance and long term impact of the region concept can be found in the monograph [3].…”

Section: Introductionmentioning

confidence: 99%

Adding A/Sync Places to the Synthesis Procedure for Whole-Place Operations Nets with Localities

Kleijn¹,

Koutny²,

Pietkiewicz-Koutny³

2017

SACS

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Assuming that the behavioural specification of a concurrent system is given in the form of a step transition system, where the arcs between states are labelled by steps (multisets of executed actions), we focus on the problem of synthesising a Petri net generating a reachability graph isomorphic to a given step transition system. To deal with step transition systems more complicated than those generated by standard Place/Transition nets, we consider in this paper Petri nets with wholeplace operations, localities, and a/sync places. We adapt and extend the general approach developed within the framework of τ -nets and the theory of regions of step transition systems. Building on the results presented in [23], emphasis here is on the role of a/sync places with their potential for an instantaneous transfer of tokens within a step. In a series of results we demonstrate the robustness of the notion of region for Petri net synthesis.

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A Trace Semantics for Petri Nets

Cited by 41 publications

References 20 publications

Abstract processes of place/transition systems

Abstract processes of place/transition systems

Mind the gap: Expanding communication options in decentralized discrete-event control

Adding A/Sync Places to the Synthesis Procedure for Whole-Place Operations Nets with Localities

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