Elementary Net Synthesis Remains NP-Complete Even for Extremely Simple Inputs

Tredup, Ronny; Rosenke, Christian; Wolf, Karsten

doi:10.1007/978-3-319-91268-4_3

Cited by 16 publications

(24 citation statements)

References 12 publications

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“…In [8], both problems have been shown to be NP-complete for pure 1-bounded P/T-nets. This has been confirmed for almost trivial inputs in [16,14]. This paper shows feasibility, ESSP and SSP to be NP-complete for b-bounded P/T-nets, b ∈ N + .…”

Section: Introductionsupporting

confidence: 64%

“…In [16,14], we have shown that a union U is a useful vehicle to investigate if A(U ) has the τ -feasibility, τ -ESSP and τ -SSP if τ = τ 1 1 . The following lemma generalizes this observation for…”

Section: Every Marking Of N R1mentioning

confidence: 99%

“…In fact, in [3] it has been shown that feasibility is NP-complete for 1-bounded P/T-nets, that is, if the bound b = 1 is chosen a priori. In [16,14], it was proven that this remains true even for strongly restricted input TSs. 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.…”

Section: Introductionmentioning

confidence: 97%

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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: 64%

Section: Every Marking Of N R1mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 97%

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Hardness Results for the Synthesis of b-bounded Petri Nets

Tredup

2019

Application and Theory of Petri Nets and Concurrency

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“…The complexity of τ -feasibility has originally been investigated for elementary net systems [1], where it is NP-complete to decide if general TSs can be synthesized. In [11,15] this has been confirmed even for considerably restricted input TSs. Further boolean net types have been investigated in [13,14], cf.…”

Section: Introductionmentioning

confidence: 64%

“…The rows 11 and 12 intersect in eight supersets of {nop, inp, out, set, res}. (13)(14)(15)(16)): Results of this paper. Notice that isomorphic types occur in the same row.…”

Section: Introductionmentioning

confidence: 99%

Tracking Down the Bad Guys: Reset and Set Make Feasibility for Flip-Flop Net Derivatives NP-complete

Tredup

2019

Electron. Proc. Theor. Comput. Sci.

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Boolean Petri nets are differentiated by types of nets τ based on which of the interactions nop, inp, out, set, res, swap, used, and free they apply or spare. The synthesis problem relative to a specific type of nets τ is to find a boolean τ -net N whose reachability graph is isomorphic to a given transition system A. The corresponding decision version of this search problem is called feasibility. Feasibility is known to be polynomial for all types of flip flop derivates defined by {nop, swap} ∪ ω, ω ⊆ {inp, out, used, free}. In this paper, we replace inp, out by res, set and show that feasibility becomes NP-complete for {nop, swap} ∪ ω if ω ⊆ {res, set, used, free} such that ω ∩ {set, res} = ∅ and ω ∩ {used, free} = ∅. The reduction guarantees a low degree for A's states and, thus, preserves hardness of feasibility even for considerable input restrictions. Type of net τ Complexity status # 1 τ = {nop, res} ∪ ω, ω ⊆ {inp, used, free} polynomial time 8 2 τ = {nop, set} ∪ ω, ω ⊆ {out, used, free} polynomial time 8 3 τ = {nop, swap} ∪ ω, ω ⊆ {inp, out, used, free} polynomial time 16 4 τ = {nop} ∪ ω, ω ⊆ {used, free} polynomial time 4 5 τ = {nop, inp, free} or τ = {nop, inp, used, free} NP-complete 2 6 τ = {nop, out, used} or τ = {nop, out, used, free} NP-complete 2 7 τ = {nop, set, res} ∪ ω, ∅ = ω ⊆ {used, free} NP-complete 3 8 τ = {nop, inp, out} ∪ ω, ω ⊆ {used, free} NP-complete 4 9 τ = {nop, inp, res, swap} ∪ ω, ω ⊆ {used, free} NP-complete 4 10 τ = {nop, out, set, swap} ∪ ω, ω ⊆ {used, free} NP-complete 4 11 τ = {nop, inp, set} ∪ ω, ω ⊆ {out,

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Indulpet Miner: Combining Discovery Algorithms

Leemans¹,

Tax²,

Hofstede³

2018

Lecture Notes in Computer Science

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In this work, we explore an approach to process discovery that is based on combining several existing process discovery algorithms. We focus on algorithms that generate process models in the process tree notation, which are sound by design. The main components of our proposed process discovery approach are the Inductive Miner, the Evolutionary Tree Miner, the Local Process Model Miner and a new bottom-up recursive technique. We conjecture that the combination of these process discovery algorithms can mitigate some of the weaknesses of the individual algorithms. In cases where the Inductive Miner results in overgeneralizing process models, the Evolutionary Tree Miner can often mine much more precise models. At the other hand, while the Evolutionary Tree Miner is computationally expensive, running it only on parts of the log that the Inductive Miner is not able to represent with a precise model fragment can considerably limit the search space size of the Evolutionary Tree Miner. Local Process Models and bottom-up recursion aid the Evolutionary Tree Miner further by instantiating it with frequent process model fragments. We evaluate our approaches on a collection of real-life event logs and find that it does combine the advantages of the miners and in some cases surpasses other discovery techniques.

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Elementary Net Synthesis Remains NP-Complete Even for Extremely Simple Inputs

Cited by 16 publications

References 12 publications

Hardness Results for the Synthesis of b-bounded Petri Nets

Hardness Results for the Synthesis of b-bounded Petri Nets

Tracking Down the Bad Guys: Reset and Set Make Feasibility for Flip-Flop Net Derivatives NP-complete

Indulpet Miner: Combining Discovery Algorithms

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