Valiant’s holant theorem and matchgate tensors

Authors:
Jin-Yi Cai;Vinay Choudhary
Affiliations:
Computer Sciences Department, University of Wisconsin, Madison, WI;Computer Sciences Department, University of Wisconsin, Madison, WI
Venue:
TAMC'06 Proceedings of the Third international conference on Theory and Applications of Models of Computation
Year:
2006

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Abstract

We propose matchgate tensors as a natural and proper language to develop Valiant’s new theory of Holographic Algorithms. We give a treatment of the central theorem in this theory—the Holant Theorem—in terms of matchgate tensors. Some generalizations are presented.