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
The complexity of theorem-proving procedures
STOC '71 Proceedings of the third annual ACM symposium on Theory of computing
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
On the Theory of Matchgate Computations
CCC '07 Proceedings of the Twenty-Second Annual IEEE Conference on Computational Complexity
Holographic algorithms with unsymmetric signatures
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Basis Collapse in Holographic Algorithms
Computational Complexity
Signature Theory in Holographic Algorithms
ISAAC '08 Proceedings of the 19th International Symposium on Algorithms and Computation
Holographic algorithms: The power of dimensionality resolved
Theoretical Computer Science
On Symmetric Signatures in Holographic Algorithms
Theory of Computing Systems - Special Issue: Theoretical Aspects of Computer Science
Matrices and Matroids for Systems Analysis
Matrices and Matroids for Systems Analysis
Approximation complexity of complex-weighted degree-two counting constraint satisfaction problems
COCOON'11 Proceedings of the 17th annual international conference on Computing and combinatorics
Guest column: complexity dichotomies of counting problems
ACM SIGACT News
Computational Complexity of Holant Problems
SIAM Journal on Computing
Gadgets and anti-gadgets leading to a complexity dichotomy
Proceedings of the 3rd Innovations in Theoretical Computer Science Conference
A dichotomy theorem for the approximate counting of complex-weighted bounded-degree Boolean CSPs
Theoretical Computer Science
Holographic algorithms on domain size k2
TAMC'12 Proceedings of the 9th Annual international conference on Theory and Applications of Models of Computation
Approximate counting for complex-weighted Boolean constraint satisfaction problems
Information and Computation
Spin systems on k-regular graphs with complex edge functions
Theoretical Computer Science
Approximation complexity of complex-weighted degree-two counting constraint satisfaction problems
Theoretical Computer Science
A complete dichotomy rises from the capture of vanishing signatures: extended abstract
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
Partition functions on k-regular graphs with {0,1}-vertex assignments and real edge functions
Theoretical Computer Science
The complexity of planar boolean #CSP with complex weights
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
The complexity of the counting constraint satisfaction problem
Journal of the ACM (JACM)
The complexity of complex weighted Boolean #CSP
Journal of Computer and System Sciences
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We develop the theory of holographic algorithms initiated by Leslie Valiant. First we define a basis manifold. Then we characterize algebraic varieties of realizable symmetric generators and recognizers on the basis manifold, and give a polynomial time decision algorithm for the simultaneous realizability problem. These results enable one to decide whether suitable signatures for a holographic algorithm are realizable, and if so, to find a suitable linear basis to realize these signatures by an efficient algorithm. Using the general machinery we are able to give unexpected 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 characterization of 2-admissibility and some general constructions of admissible and realizable families.