Algorithmic number theory
The Complexity of Counting in Sparse, Regular, and Planar Graphs
SIAM Journal on Computing
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
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
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 with unsymmetric signatures
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Holographic algorithms: guest column
ACM SIGACT News
Basis Collapse in Holographic Algorithms
Computational Complexity
Time-Space Tradeoffs for Counting NP Solutions Modulo Integers
Computational Complexity
Holographic algorithms: The power of dimensionality resolved
Theoretical Computer Science
Holant problems and counting CSP
Proceedings of the forty-first annual ACM symposium on Theory of computing
A Computational Proof of Complexity of Some Restricted Counting Problems
TAMC '09 Proceedings of the 6th Annual Conference on Theory and Applications of Models of Computation
Classification of a Class of Counting Problems Using Holographic Reductions
COCOON '09 Proceedings of the 15th Annual International Conference on Computing and Combinatorics
On blockwise symmetric signatures for matchgates
Theoretical Computer Science
Journal of Symbolic Computation
Graph homomorphisms with complex values: a dichotomy theorem
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Holographic reduction: a domain changed application and its partial converse theorems
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
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
Approximate counting for complex-weighted Boolean constraint satisfaction problems
WAOA'10 Proceedings of the 8th international conference on Approximation and online algorithms
A computational proof of complexity of some restricted counting problems
Theoretical Computer Science
Holographic reduction for some counting problems
Information Processing Letters
Progress in complexity of counting problems
FAW-AAIM'11 Proceedings of the 5th joint international frontiers in algorithmics, and 7th international conference on Algorithmic aspects in information and management
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
Some observations on holographic algorithms
LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
Dichotomy for Holant problems of Boolean domain
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
A dichotomy for k-regular graphs with {0, 1}-vertex assignments and real edge functions
TAMC'10 Proceedings of the 7th annual conference on Theory and Applications of Models of Computation
Holographic algorithms: the power of dimensionality resolved
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
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We develop the theory of holographic algorithms. We definea basis manifold and give characterizations of algebraic varieties of realizable symmetric generators and recognizers on this manifold. We present a polynomial time decision algorithm for the simultaneous realizability problem. Using the general machinery we are able to giveunexpected holographic algorithms for some counting problems, modulo certain Mersenne type integers. These counting problems are P-complete without the moduli. Going beyond symmetric signatures, we define d-admissibility and d-realizability for general signatures, and give a characterizationof 2-admissibility.