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- W105846551 abstract "We establish a 1-1 correspondence between Valiant’s character theory of matchgate/matchcircuit [14] and his signature theory of planar-matchgate/matchgrid [16], thus unifying the two theories in expressibility. In [3], we had established a complete characterization of general matchgates, in terms of a set of useful Grassmann-Plücker identities. With this correspondence, we give a corresponding set of identities which completely characterizes planar-matchgates and their signatures. Applying this characterization we prove some negative results for holographic algorithms. On the positive side, we also give a polynomial time algorithm for a simultaneous node-edge deletion problem, using holographic algorithms. Finally we give characterizations of symmetric signatures realizable in the Hadamard basis." @default.
- W105846551 created "2016-06-24" @default.
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- W105846551 date "2006-01-01" @default.
- W105846551 modified "2023-10-16" @default.
- W105846551 title "Some Results on Matchgates and Holographic Algorithms" @default.
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- W105846551 doi "https://doi.org/10.1007/11786986_61" @default.
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