Quantum Circuits That Can Be Simulated Classically in Polynomial Time
SIAM Journal on Computing
Theoretical Computer Science
A Combinatorial Proof of Kneser’s Conjecture
Combinatorica
Holographic Algorithms (Extended Abstract)
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Holographic algorithms: from art to science
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Bases Collapse in Holographic Algorithms
CCC '07 Proceedings of the Twenty-Second Annual IEEE Conference on Computational Complexity
On the Theory of Matchgate Computations
CCC '07 Proceedings of the Twenty-Second Annual IEEE Conference on Computational Complexity
On symmetric signatures in holographic algorithms
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
Matrices and Matroids for Systems Analysis
Matrices and Matroids for Systems Analysis
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Completeness for parity problems
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
Valiant’s holant theorem and matchgate tensors
TAMC'06 Proceedings of the Third international conference on Theory and Applications of Models of Computation
Some results on matchgates and holographic algorithms
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
Holographic algorithms: the power of dimensionality resolved
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
Holographic algorithms: From art to science
Journal of Computer and System Sciences
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Holographic algorithms were introduced by Valiant as a new methodology to derive polynomial time algorithms. Here information and computation are represented by exponential sums using the so-called signatures. These signatures express superpositions of perfect matchings, and are used to achieve exponential sized cancellations, and thereby exponential speedups. Most holographic algorithms so far used symmetric signatures. In this paper we use unsymmetric signatures to give some new holographic algorithms. We also prove a characterization theorem for a class of realizable un-symmetric signatures, each of which may be used to design new holographic algorithms.