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Parameterized Complexity of Synthesizing b-Bounded (m, n)-T-Systems

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SOFSEM 2020: Theory and Practice of Computer Science (SOFSEM 2020)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12011))

Abstract

Let \(b\in \mathbb {N}^+\). Synthesis of pure b-bounded (m, n)-T-systems ((m,n)-Synthesis, for short) consists in deciding whether there exists for an input (A, m, n) 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 \(m+n\).

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Acknowledgements

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

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Authors and Affiliations

  1. Universität Rostock, Institut für Informatik, Theoretische Informatik, Albert-Einstein-Straße 22, 18059, Rostock, Germany

    Ronny Tredup

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  1. Ronny Tredup
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Correspondence to Ronny Tredup .

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Editors and Affiliations

  1. University of Macedonia, Thessaloniki, Greece

    Alexander Chatzigeorgiou

  2. University of Bergamo, Bergamo, Italy

    Riccardo Dondi

  3. Cyprus University of Technology, Limassol, Cyprus

    Herodotos Herodotou

  4. Carnegie Mellon University Qatar, Doha, Qatar

    Christos Kapoutsis

  5. Open University of Cyprus, Nicosia, Cyprus

    Yannis Manolopoulos

  6. University of Cyprus, Nicosia, Cyprus

    George A. Papadopoulos

  7. Paris Dauphine University, Paris, France

    Florian Sikora

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Tredup, R. (2020). Parameterized Complexity of Synthesizing b-Bounded (m, n)-T-Systems. In: Chatzigeorgiou, A., et al. SOFSEM 2020: Theory and Practice of Computer Science. SOFSEM 2020. Lecture Notes in Computer Science(), vol 12011. Springer, Cham. https://doi.org/10.1007/978-3-030-38919-2_19

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  • DOI: https://doi.org/10.1007/978-3-030-38919-2_19

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-38918-5

  • Online ISBN: 978-3-030-38919-2

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