Signature Theory in Holographic Algorithms

Authors:
Jin-Yi Cai;Pinyan Lu
Affiliations:
Computer Sciences Department, University of Wisconsin, Madison, USA WI 53706;Institute for Theoretical Computer Science, Tsinghua University, Beijing, P.R. China 100084
Venue:
ISAAC '08 Proceedings of the 19th International Symposium on Algorithms and Computation
Year:
2008

Citing 0
Cited 6

Holographic algorithms: From art to science

Journal of Computer and System Sciences
A trichotomy theorem for the approximate counting of complex-weighted bounded-degree boolean CSPs

COCOA'10 Proceedings of the 4th international conference on Combinatorial optimization and applications - Volume Part I
The complexity of symmetric Boolean parity Holant problems

ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
A dichotomy theorem for the approximate counting of complex-weighted bounded-degree Boolean CSPs

Theoretical Computer Science
Approximate counting for complex-weighted Boolean constraint satisfaction problems

Information and Computation
Approximation complexity of complex-weighted degree-two counting constraint satisfaction problems

Theoretical Computer Science

Quantified Score

Hi-index	0.00

Visualization

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.