Synthesis of Structurally Restricted b-bounded Petri Nets: Complexity Results

Tredup, Ronny

doi:10.1007/978-3-030-30806-3_16

Cited by 10 publications

(4 citation statements)

References 16 publications

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“…This can easily be shown by a trivial reduction from the unrestricted to the restricted problem. In [28], it has been shown that ERS, formulated for b-bounded Petri nets, is NP-complete even if κ = 1. Moreover, in [29], it has been argued that the corresponding problem, although being in XP, is W [1]hard for these nets, when ̺ + κ is considered as a parameter.…”

Section: Introductionmentioning

confidence: 99%

Synthesis of Pure and Impure Petri nets With Restricted Place-environments: Complexity Issues

Devillers¹,

Tredup²

2021

Preprint

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Petri net synthesis consists in deciding for a given transition system A whether there exists a Petri net N whose reachability graph is isomorphic to A. Several works examined the synthesis of Petri net subclasses that restrict, for every place p of the net, the cardinality of its preset or of its postset or both in advance by small natural numbers ̺ and κ, respectively, such as for example (weighted) marked graphs, (weighted) T-systems and choice-free nets. In this paper, we study the synthesis aiming at Petri nets which have such restricted place environments, from the viewpoint of classical and parameterized complexity: We first show that, for any fixed natural numbers ̺ and κ, deciding whether for a given transition system A there is a Petri net N such that (1) its reachability graph is isomorphic to A and (2) for every place p of N the preset of p has at most ̺ and the postset of p has at most κ elements is doable in polynomial time. Secondly, we introduce a modified version of the problem, namely ENVIRONMENT RESTRICTED SYNTHESIS (ERS, for short), where ̺ and κ are part of the input, and show that ERS is NPcomplete, regardless whether the sought net is impure or pure. In case of the impure nets, our methods also imply that ERS parameterized by ̺ + κ is W [2]-hard.

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Section: Introductionmentioning

confidence: 99%

Synthesis of Pure and Impure Petri nets With Restricted Place-environments: Complexity Issues

Devillers¹,

Tredup²

2021

Preprint

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“…On the other hand, the results on synthesis of k-bounded (never more than k tokens on a place) [20], safe (1-bounded) and elementary nets [3] investigate classes which are defined through behavioral restrictions. Further, generalized settings of the synthesis problem for these and some other classes were studied [21], and NP-completeness results for many of them were presented. In contrast to this multitude of P/T net classes, for Boolean nets, only the constrains for the set of interactions have appeared in the literature, deriving for instance flip-flop nets [17], trace nets [5], inhibitor nets [14].…”

Section: Introductionmentioning

confidence: 99%

On the Parameterized Complexity of Synthesizing Boolean Petri Nets With Restricted Dependency

Tredup

Erofeev

2020

Electron. Proc. Theor. Comput. Sci.

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Modeling of real-world systems with Petri nets allows to benefit from their generic concepts of parallelism, synchronisation and conflict, and obtain a concise yet expressive system representation. Algorithms for synthesis of a net from a sequential specification enable the well-developed theory of Petri nets to be applied for the system analysis through a net model. The problem of τ-synthesis consists in deciding whether a given directed labeled graph A is isomorphic to the reachability graph of a Boolean Petri net N of type τ. In case of a positive decision, N should be constructed. For many Boolean types of nets, the problem is NP-complete. This paper deals with a special variant of τ-synthesis that imposes restrictions for the target net N: we investigate dependency d-restricted τ-synthesis (DRτS) where each place of N can influence and be influenced by at most d transitions. For a type τ, if τ-synthesis is NP-complete then DRτS is also NP-complete. In this paper, we show that DRτS parameterized by d is in XP. Furthermore, we prove that it is W [2]-hard, for many Boolean types that allow unconditional interactions set and reset.

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“…On the other hand, the results on synthesis of k-bounded (never more than k tokens on a place) [20], safe (1-bounded) and elementary nets [3] investigate classes which are defined through behavioral restrictions. Further, generalized settings of the synthesis problem for these and some other classes was studied [21], and NP-completeness results for many of them were presented. In contrast to this multitude of P/T net classes, for Boolean nets, only the constrains for the set of interactions have appeared in the literature, deriving for instance flip-flop nets [17], trace nets [5], inhibitor nets [14].…”

Section: Introductionmentioning

confidence: 99%

On the Parameterized Complexity of Synthesizing Boolean Petri Nets With Restricted Dependency (Technical Report)

Tredup,

Erofeev

2020

Preprint

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The problem of τ -synthesis consists in deciding whether a given directed labeled graph A is isomorphic to the reachability graph of a Boolean Petri net N of type τ . In case of a positive decision, N should be constructed. For many Boolean types of nets, the problem is NP-complete. This paper deals with a special variant of τ -synthesis that imposes restrictions for the target net N : we investigate dependency d-restricted τ -synthesis (DRτ S) where each place of N can influence and be influenced by at most d transitions. For a type τ , if τsynthesis is NP-complete then DRτ S is also NP-complete. In this paper, we show that DRτ S parameterized by d is in XP. Furthermore, we prove that it is W [2]-hard, for many Boolean types that allow unconditional interactions set and reset.

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Synthesis of Structurally Restricted b-bounded Petri Nets: Complexity Results

Cited by 10 publications

References 16 publications

Synthesis of Pure and Impure Petri nets With Restricted Place-environments: Complexity Issues

Synthesis of Pure and Impure Petri nets With Restricted Place-environments: Complexity Issues

On the Parameterized Complexity of Synthesizing Boolean Petri Nets With Restricted Dependency

On the Parameterized Complexity of Synthesizing Boolean Petri Nets With Restricted Dependency (Technical Report)

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