Generating all minimal petri net unsolvable binary words

Erofeev, Evgeny; Barylska, Kamila; Mikulski, Łukasz; Piatkowski, Marcin

doi:10.1016/j.dam.2019.04.023

Cited by 5 publications

(7 citation statements)

References 4 publications

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“…reveals that s 2 is in the convex hull of S a and therefore, a ought to be enabled at s 2 . The special case of words over just two letters (like abbaa) has been analysed in [34,35,36]. We have several characterisations of the PN-unsolvable amongst them, either based on letter-counting, or based on pattern-matching, or based on deriving all of them by syntactic rules from a set of basic unsolvable words.…”

Section: Targeting Nets With Linear Reachability Graphsmentioning

confidence: 99%

Target-oriented Petri Net Synthesis

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Devillers

Erofeev

et al. 2020

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When a Petri net is synthesised from a labelled transition system, it is frequently desirable that certain additional constraints are fulfilled. For example, in circuit design, one is often interested in constructing safe Petri nets. Targeting such subclasses of Petri nets is not necessarily computationally more efficient than targeting the whole class. For example, targeting safe nets is known to be NP-complete while targeting the full class of place/transition nets is polynomial, in the size of the transition system. In this paper, several classes of Petri nets are examined, and their suitability for being targeted through efficient synthesis from labelled transition systems is studied and assessed. The focus is on choice-free Petri nets and some of their subclasses. It is described how they can be synthesised efficiently from persistent transition systems, summarising and streamlining in tutorial style some of the authors’ and their groups’ work over the past few years.

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Section: Targeting Nets With Linear Reachability Graphsmentioning

confidence: 99%

Target-oriented Petri Net Synthesis

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Devillers

Erofeev

et al. 2020

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“…More recently, another kind of restriction has been considered, limiting the number of different transition labels of the LTS in combination with restrictions on the LTS structure: for the binary case, feasibility of net synthesis from finite linear LTS and LTS with cycles 4 has been characterised by rates of labels in the transition system [2,3] and by pseudo-regular expressions [17], giving rise to fast specialised synthesis algorithms; moreover, a complete enumeration of the shapes of synthesisable transition systems is presented in [18].…”

Section: Introductionmentioning

confidence: 99%

“…not containing any node twice) and cycles (i.e. closed paths, whose start and end states are equal), often induces simple conditions of unsolvability for the entire LTS, as highlighted in other works [2,17,4]. Moreover, cycles appear systematically in the reachability graph of live and/or reversible Petri nets [27,22], which are used to model various real-world applications, such as embedded systems [19].…”

Section: Introductionmentioning

confidence: 99%

Synthesis of Weighted Marked Graphs from Constrained Labelled Transition Systems: A Geometric Approach

Devillers¹,

Erofeev²,

Hujsa³

2019

Transactions on Petri Nets and Other Models of Concurrency XIV

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Recent studies investigated the problems of analysing Petri nets and synthesising them from labelled transition systems (LTS) with two labels (transitions) only. In this paper, we extend these works by providing new conditions for the synthesis of Weighted Marked Graphs (WMGs), a well-known and useful class of weighted Petri nets in which each place has at most one input and one output. Some of these new conditions do not restrict the number of labels; the other ones consider up to 3 labels. Additional constraints are investigated: when the LTS is either finite or infinite, and either cyclic or acyclic. We show that one of these conditions, developed for 3 labels, does not extend to 4 nor to 5 labels. Also, we tackle geometrically the WMG-solvability of finite, acyclic LTS with any number of labels.

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“…In [3] only the sequential (interleaving) semantics of nets was considered and, in fact, several of the presented examples were just (nite) trace systems, taking advantage of the results presented in [2,12], where binary words representable by Petri net were characterised. The latter problem and its consequences for reversibility has been recently further investigated in [11].…”

Section: Introductionmentioning

confidence: 99%

Reversing Steps in Petri Nets

Frutos-Escrig

Koutny

Mikulski

2019

Application and Theory of Petri Nets and Concurrency

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In reversible computations one is interested in the development of mechanisms allowing to undo the eects of executed actions. The past research has been concerned mainly with reversing single actions. In this paper, we consider the problem of reversing the eect of the execution of groups of actions (steps). Using Petri nets as a system model, we introduce concepts related to this new scenario, generalising notions used in the single action case. We then present a number of properties which arise in the context of reversing of steps of executed transitions in place/transition nets. We obtain both positive and negative results, showing that dealing with steps makes reversibility more involved than in the sequential case. In particular, we demonstrate that there is a crucial dierence between reversing steps which are sets and those which are true multisets.

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Generating all minimal petri net unsolvable binary words

Cited by 5 publications

References 4 publications

Target-oriented Petri Net Synthesis

Target-oriented Petri Net Synthesis

Synthesis of Weighted Marked Graphs from Constrained Labelled Transition Systems: A Geometric Approach

Reversing Steps in Petri Nets

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