Canonical Prefixes of Petri Net Unfoldings

Khomenko, Victor; Koutny, Maciej; Vogler, Walter

doi:10.1007/3-540-45657-0_49

Cited by 60 publications

(89 citation statements)

References 13 publications

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“…Both problems were overcome in the next years. Improved algorithms for constructing complete prefixes were described in [49,22,23,31,32,35,36,38,24], and extensions to (almost) arbitrary properties expressible in Linear Temporal Logic (LTL) were presented in [16,19,20].Since 2000 the algorithms for constructing complete prefixes have been parallelized [33,55] and distributed [5]. Initially developed for systems modeled as "plain" Petri nets, the unfolding approach has been extended to high-level Petri nets [37,55] [3,2].…”

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A False History of True Concurrency: From Petri to Tools

Esparza

2010

Model Checking Software

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Abstract. I briefly review the history of the unfolding approach to model checking.Carl Adam Petri passed away on July 2, 2010. I learnt about his death three days later, a few hours after finishing this text. He was a very profound and highly original thinker, and will be sadly missed. This note is dedicated to his memory.In some papers and talks, Moshe Vardi has described the history of the automatatheoretic approach to model checking, the verification technique that inspired the SPIN model checker and other tools. He traces it back to the work of theoreticians like Büchi, Prior, Trakhtenbrot and others, whose motivations were surprisingly far away from the applications that their ideas found down the line. Inspired by this work, in this note I briefly present the origins of the unfolding approach to model checking [21], a branch of the automata-theoretic approach that alleviates the state-explosion problem caused by concurrency.Since the unfolding approach is based on the theory of true concurrency, describing its origins requires to speak about the origin of true concurrency itself. However, here I only touch upon those aspects of the theory that directly inspired the unfolding approach. This leaves many important works out, and so this is a very partial and "false" history of true concurrency.The theory of true concurrency starts with two fundamental contributions by Carl Adam Petri, described in detail by Brauer and Reisig in an excellent article [11]. Both were a result of Petri's interest in analyzing the connection between mathematical, abstract computing machines, and their physical realizations. In his dissertation "Kommunikation mit Automaten", defended in 1962, Petri observes that the performance of a physically implemented Turing machine will degrade over time if the machine uses more and more storage space, because in this case signals have to travel longer and longer distances over longer and longer wires. To solve this problem he proposes an asynchronous architecture in which the storage space can be extended while the machine continues to operate. In the dissertation this abstract machine is described with the help of several semi-formal representations, but three years later Petri has already distilled the first mathematical formalism for asynchronous computation, and, arguably, the beginning of concurrency theory: Petri nets.Petri's second contribution is an analysis of the notion of execution of a machine as a sequence of global states, or as a sequence of events ordered by their occurrence times with respect to some global clock. He observes that global states or global clocks are again a mathematical construct that cannot be "implemented": since information can only travel at finite speed, no part of a system can know the state of all its components at a certain moment in time. 1 He proposes to replace executions by nonsequential processes, sets of events ordered not by the time at which they occur, but by the causality relation, which is independent of the observer. The theory of nonseque...

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A False History of True Concurrency: From Petri to Tools

Esparza

2010

Model Checking Software

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“…In this section, we first present basic definitions concerning Petri nets and STGs, and then recall notions related to unfolding prefixes (see also [ERV02,Kho03,Mur89]). …”

Section: Basic Definitionsmentioning

confidence: 99%

“…Efficient algorithms exist for building such prefixes [ERV02,Kho03], which ensure that the number of non-cut-off events in a complete prefix can never exceed the number of reachable states of Γ. However, complete prefixes are often exponentially smaller than the corresponding state graphs, especially for highly concurrent Petri nets, because they represent concurrency directly rather than by multidimensional 'diamonds' as it is done in state graphs.…”

Section: Unfolding Prefixesmentioning

confidence: 99%

“…Since in practice STGs usually exhibit a lot of concurrency, but have rather few choice points, their complete unfolding prefixes are often exponentially smaller than the corresponding state graphs; in fact, in many of the experiments conducted in [Kho03,KKY04] they are just slightly bigger then the original STGs themselves. Therefore, unfolding prefixes are well-suited for both visualisation of an STG's behaviour and alleviating the state space explosion problem.…”

Section: Introductionmentioning

confidence: 99%

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Combining Decomposition and Unfolding for STG Synthesis

Khomenko

Schaefer

Petri Nets and Other Models of Concurrency – ICATPN 2007

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Modeling Multi-valued Genetic Regulatory Networks Using High-Level Petri Nets

Comet

Klaudel

Liauzu

2005

Applications and Theory of Petri Nets 2005

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Regulatory networks are at the core of all biological functions from biochemical pathways to gene regulation and cell communication processes. Because of the complexity of the interweaving retroactions, the overall behavior is difficult to grasp and the development of formal methods is needed in order to confront the supposed properties of the biological system to the model. We revisit here the tremendous work of R. Thomas and show that its binary and also its multi-valued approach can be expressed in a unified way with high-level Petri nets. A compact modeling of genetic networks is proposed in which the tokens represent gene's expression levels and their dynamical behavior depends on a certain number of biological parameters. This allows us to take advantage of techniques and tools in the field of high-level Petri nets. A developed prototype lets a biologist to verify systematically the coherence of the system under various hypotheses. These hypotheses are translated into temporal logic formulae and the model-checking techniques are used to retain only the models whose behavior is coherent with the biological knowledge.

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Canonical Prefixes of Petri Net Unfoldings

Cited by 60 publications

References 13 publications

A False History of True Concurrency: From Petri to Tools

A False History of True Concurrency: From Petri to Tools

Combining Decomposition and Unfolding for STG Synthesis

Modeling Multi-valued Genetic Regulatory Networks Using High-Level Petri Nets

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