Proceedings of the forty-first annual ACM symposium on Theory of computing
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
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
Approximation complexity of complex-weighted degree-two counting constraint satisfaction problems
COCOON'11 Proceedings of the 17th annual international conference on Computing and combinatorics
Spin systems on graphs with complex edge functions and specified degree regularities
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
Dichotomy for Holant problems of Boolean domain
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Classical simulation and complexity of quantum computations
CSR'10 Proceedings of the 5th international conference on Computer Science: theory and Applications
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
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 complex weighted Boolean #CSP
Journal of Computer and System Sciences
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Complexity theory is built fundamentally on the notion of efficient reduction among computational problems. Classical reductions involve gadgets that map solution fragments of one problem to solution fragments of another in one-to-one, or possibly one-to-many, fashion. In this paper we propose a new kind of reduction that allows for gadgets with many-to-many correspondences, in which the individual correspondences among the solution fragments can no longer be identified. Their objective may be viewed as that of generating interference patterns among these solution fragments so as to conserve their sum. We show that such holographic reductions provide a method of translating a combinatorial problem to finite systems of polynomial equations with integer coefficients such that the number of solutions of the combinatorial problem can be counted in polynomial time if one of the systems has a solution over the complex numbers. We derive polynomial time algorithms in this way for a number of problems for which only exponential time algorithms were known before. General questions about complexity classes can also be formulated. If the method is applied to a P-complete problem, then polynomial systems can be obtained, the solvability of which would imply P$^{{\tiny{\#P}}}$ = NC2.