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Parameterized Complexity of Synthesizing b-Bounded (mn)-T-Systems

  • Ronny TredupEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 12011)

Abstract

Let \(b\in \mathbb {N}^+\). Synthesis of pure b-bounded (mn)-T-systems ((m,n)-Synthesis, for short) consists in deciding whether there exists for an input (Amn) of transition system A and integers \(m,n\in \mathbb {N}\) a pure b-bounded Petri net N as follows: N’s reachability graph is isomorphic to A, and each of N’s places has at most m incoming and at most n outgoing transitions. In the event of a positive decision, N should be constructed. The problem is known to be NP-complete, and (m,n)-Synthesis parameterized by \(m+n\) is in XP [14]. In this paper, we enhance our understanding of (m,n)-Synthesis from the viewpoint of parameterized complexity by showing that it is W[1]-hard when parameterized by \(m+n\).

Notes

Acknowledgements

I’m grateful to the reviewers for their helpful comments.

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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Universität Rostock, Institut für Informatik, Theoretische InformatikRostockGermany

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