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Signature Theory in Holographic Algorithms

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Algorithms and Computation (ISAAC 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5369))

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Abstract

Valiant initiated a theory of holographic algorithms based on perfect matchings. These algorithms express computations in terms of signatures realizable by matchgates. We substantially develop the signature theory in terms of d-realizability and d-admissibility, where d measures the dimension of the basis subvariety on which a signature is feasible. Starting with 2-admissibility, we prove a Birkhoff-type theorem for the class of 2-realizable signatures. This gives a complete structural understanding of 2-realizability and 2-admissibility. This is followed by characterization theorems for 1-realizability and 1-admissibility.

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References

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Author information

Authors and Affiliations

  1. Computer Sciences Department, University of Wisconsin, Madison, WI 53706, USA

    Jin-Yi Cai

  2. Institute for Theoretical Computer Science, Tsinghua University, Beijing, 100084, P.R. China

    Pinyan Lu

Authors
  1. Jin-Yi Cai
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  2. Pinyan Lu
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Editor information

Editors and Affiliations

  1. School of Information Technologies, University of Sydney, Australia

    Seok-Hee Hong

  2. Graduate School of Informatics, Kyoto University, 606-8501, Kyoto, Japan

    Hiroshi Nagamochi

  3. Graduate School of Informatics, Kyoto University, Japan

    Takuro Fukunaga

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© 2008 Springer-Verlag Berlin Heidelberg

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Cai, JY., Lu, P. (2008). Signature Theory in Holographic Algorithms. In: Hong, SH., Nagamochi, H., Fukunaga, T. (eds) Algorithms and Computation. ISAAC 2008. Lecture Notes in Computer Science, vol 5369. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-92182-0_51

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  • DOI: https://doi.org/10.1007/978-3-540-92182-0_51

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-92181-3

  • Online ISBN: 978-3-540-92182-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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