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Erschienen in:
2008 | OriginalPaper | Buchkapitel
Signature Theory in Holographic Algorithms
verfasst von : Jin-Yi Cai, Pinyan Lu
Erschienen in: Algorithms and Computation
Verlag: Springer Berlin Heidelberg
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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.