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No Small Nondeterministic Read-Once Branching Programs for CNFs of Bounded Treewidth

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Parameterized and Exact Computation (IPEC 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8894))

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Abstract

In this paper, given a parameter \(k\), we demonstrate an infinite class of cnfs of treewidth at most \(k\) of their primal graphs such that equivalent nondeterministic read-once branching programs (nrobps) are of size at least \(n^{ck}\) for some universal constant \(c\). Thus we rule out the possibility of fixed-parameter tractable space complexity of nrobps parameterized by the smallest treewidth of equivalent cnfs.

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Notes

  1. 1.

    Notice that on the nrobp in Figure 1, there is a path where \(v_2\) occurs before \(v_3\) and a path where \(v_3\) occurs before \(v_2\). Thus this nrobp, although uniform, is not oblivious.

  2. 2.

    We sometimes treat sequences as sets, the correct use will be always clear from the context.

References

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Acknowledgments

I would like to thank anonymous reviewers for very useful and insightful comments. The research has been partly supported by the EPSRC grant EP/L020408/1.

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Authors and Affiliations

  1. Department of Computer Science and Information Systems, Birkbeck, University of London, London, UK

    Igor Razgon

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  1. Igor Razgon
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Correspondence to Igor Razgon .

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Editors and Affiliations

  1. Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, Warsaw, Poland

    Marek Cygan

  2. University of Bergen, Bergen, Norway

    Pinar Heggernes

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Razgon, I. (2014). No Small Nondeterministic Read-Once Branching Programs for CNFs of Bounded Treewidth. In: Cygan, M., Heggernes, P. (eds) Parameterized and Exact Computation. IPEC 2014. Lecture Notes in Computer Science(), vol 8894. Springer, Cham. https://doi.org/10.1007/978-3-319-13524-3_27

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  • DOI: https://doi.org/10.1007/978-3-319-13524-3_27

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-13523-6

  • Online ISBN: 978-3-319-13524-3

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