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Small Vertex Cover Makes Petri Net Coverability and Boundedness Easier

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Parameterized and Exact Computation (IPEC 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6478))

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Abstract

The coverability and boundedness problems for Petri nets are known to be Expspace-complete. Given a Petri net, we associate a graph with it. With the vertex cover number k of this graph and the maximum arc weight W as parameters, we show that coverability and boundedness are in ParaPspace. This means that these problems can be solved in space \(\mathcal{O}(ef(k,W)poly(n))\) where ef(k,W) is some exponential function and \(\mathrm{\mathit{poly}}(n)\) is some polynomial in the size of the input. We then extend the ParaPspace result to model checking a logic that can express some generalizations of coverability and boundedness.

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Authors and Affiliations

  1. The Institute of Mathematical Sciences, Chennai, India

    M. Praveen

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  1. M. Praveen
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Editors and Affiliations

  1. The Institute of Mathematical Sciences, Chennai, India

    Venkatesh Raman

  2. The Institute of Mathematical Sciences, 600113, Chennai, India

    Saket Saurabh

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Praveen, M. (2010). Small Vertex Cover Makes Petri Net Coverability and Boundedness Easier. In: Raman, V., Saurabh, S. (eds) Parameterized and Exact Computation. IPEC 2010. Lecture Notes in Computer Science, vol 6478. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17493-3_21

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  • DOI: https://doi.org/10.1007/978-3-642-17493-3_21

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-17492-6

  • Online ISBN: 978-3-642-17493-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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