The Complexity of Synthesis for 43 Boolean Petri Net Types

Tredup, Ronny; Rosenke, Christian

doi:10.1007/978-3-030-14812-6_38

Cited by 10 publications

(17 citation statements)

References 18 publications

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“…In contrast, [12] shows that it suffices to extend pure 1-bounded P/Tnets by the additive group Z 2 of integers modulo 2 to bring the complexity of synthesis down to polynomial time. The work of [15] confirms also for other types of 1-bounded Petri nets that the presence or absence of interactions between places and transitions tip the scales of synthesis complexity. However, some questions in the area of synthesis for Petri nets are still open.…”

Section: Introductionsupporting

confidence: 61%

Hardness Results for the Synthesis of b-bounded Petri Nets

Tredup

2019

Application and Theory of Petri Nets and Concurrency

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Synthesis for a type τ of Petri nets is the following search problem: For a transition system A, find a Petri net N of type τ whose state graph is isomorphic to A, if there is one. To determine the computational complexity of synthesis for types of bounded Petri nets we investigate their corresponding decision version, called feasibility. We show that feasibility is NP-complete for (pure) b-bounded P/T-nets if b ∈ N + . We extend (pure) b-bounded P/T-nets by the additive group Z b+1 of integers modulo (b + 1) and show feasibility to be NP-complete for the resulting type. To decide if A has the event state separation property is shown to be NP-complete for (pure) b-bounded and group extended (pure) bbounded P/T-nets. Deciding if A has the state separation property is proven to be NP-complete for (pure) b-bounded P/T-nets.

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Section: Introductionsupporting

confidence: 61%

Hardness Results for the Synthesis of b-bounded Petri Nets

Tredup

2019

Application and Theory of Petri Nets and Concurrency

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“…Secondly, in [8], Schmitt extended the type τ 1 P P T by the additive group of integers modulo 2, which leads to the tractable (super-) type to τ 1 ZP P T . Moreover, in [9], we argued that Schmitts approach transferred to τ 1 P T yields the tractable type τ 1 ZP T . However, by Theorem 4.…”

Section: Polynomial Time Resultsmentioning

confidence: 93%

“…The result of [8] shows that this suffices to bring the complexity of synthesis down to polynomial time. In [9,10], we progressed the approach of examining the effects of the presence and absence of different interactions on the complexity of synthesis for the broader class of Boolean Petri nets that enable independence between places and transitions. This class also contains the type of 1-bounded P/T-nets and its Z 2 -extension.…”

Section: Introductionmentioning

confidence: 99%

“…This class also contains the type of 1-bounded P/T-nets and its Z 2 -extension. Although [9,10] show that synthesis remains hard for 75 of the 128 possible Boolean types (allowing independence), [9] also discovers 36 types for which synthesis is doable in polynomial time. The latter applies in particular for the Z 2 extension of 1-bounded P/Tnets.…”

Section: Introductionmentioning

confidence: 99%

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The Complexity of Synthesis of $b$-Bounded Petri Nets

Tredup¹

2021

Preprint

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For a fixed type of Petri nets τ , τ -SYNTHESIS is the task of finding for a given transition system A a Petri net N of type τ (τ -net, for short) whose reachability graph is isomorphic to A if there is one. The decision version of this search problem is called τ -SOLVABILITY. If an input A allows a positive decision, then it is called τ -solvable and a sought net N τ -solves A. As a well known fact, A is τ -solvable if and only if it has the so-called τ -event state separation property (τ -ESSP, for short) and the τ -state separation property (τ -SSP, for short). The question whether A has the τ -ESSP or the τ -SSP defines also decision problems. In this paper, for all b ∈ N, we completely characterize the computational complexity of τ -SOLVABILITY, τ -ESSP and τ -SSP for the types of pure b-bounded Place/Transition-nets, the b-bounded Place/Transitionnets and their corresponding Z b+1 -extensions.

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“…These opposing results motivate the question which interactions of I make the synthesis problem hard and which make it tractable. In our previous work of [12,15,16], we answer this question partly and reveal the computational complexity of 120 of the 128 types that allow nop.…”

Section: Introductionmentioning

confidence: 93%