Signature Theory in Holographic Algorithms

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


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.


Polynomial Time Signature Theory Truth Assignment Basis Manifold Satisfying Assignment 
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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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