Progress in computational complexity theory
Journal of Computer Science and Technology
Holographic algorithms: from art to science
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
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
On symmetric signatures in holographic algorithms
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
Maximum edge-disjoint paths problem in planar graphs
TAMC'07 Proceedings of the 4th international conference on Theory and applications of models of computation
On the expressive power of planar perfect matching and permanents of bounded treewidth matrices
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
Journal of Symbolic Computation
Holographic algorithms: From art to science
Journal of Computer and System Sciences
A computational proof of complexity of some restricted counting problems
Theoretical Computer Science
Holographic reduction for some counting problems
Information Processing Letters
The complexity of the cover polynomials for planar graphs of bounded degree
MFCS'11 Proceedings of the 36th international conference on Mathematical foundations of computer science
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
#3-Regular bipartite planar vertex cover is #p-complete
TAMC'06 Proceedings of the Third international conference on Theory and Applications of Models of Computation
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
Some results on matchgates and holographic algorithms
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
On block-wise symmetric signatures for matchgates
FCT'07 Proceedings of the 16th international conference on Fundamentals of Computation Theory
Holographic algorithms: the power of dimensionality resolved
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
Counting matchings of size k is # W[1]-hard
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
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We introduce a new notion of efficient reduction among computational problems. Classical reductions involve gadgets that map local solutions of one problem to local solutions of another in one-to-one, or possibly many-to-one or one-to-many, fashion. Our proposed reductions allow for gadgets with many-to-many correspondences. Their objective is to preserve the sum of the local solutions. Such reductions provide a method of translating a combinatorial problem to a family of 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 some system in the family has a solution over the complex numbers. We can derive polynomial time algorithms in this way for ten problems for which only exponential time algorithms were known before. General questions about complexity classes are also formulated. If the method is applied to a #P-complete problem then we obtain families of polynomial systems such that the solvability of any one member would imply P^(#P) = NC2.