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Signature Theory in Holographic Algorithms

  • Jin-Yi Cai
  • Pinyan Lu
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5369)

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.

Keywords

Polynomial Time Signature Theory Truth Assignment Basis Manifold Satisfying Assignment 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Jin-Yi Cai
    • 1
  • Pinyan Lu
    • 2
  1. 1.Computer Sciences DepartmentUniversity of WisconsinMadisonUSA
  2. 2.Institute for Theoretical Computer ScienceTsinghua UniversityBeijingP.R. China

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