Complexity of generalized satisfiability counting problems
Information and Computation
The complexity of counting graph homomorphisms
Proceedings of the ninth international conference on on Random structures and algorithms
The Complexity of Counting in Sparse, Regular, and Planar Graphs
SIAM Journal on Computing
The complexity of partition functions
Theoretical Computer Science - Automata, languages and programming: Algorithms and complexity (ICALP-A 2004)
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 counting homomorphisms to directed acyclic graphs
Journal of the ACM (JACM)
SIAM Journal on Computing
The Complexity of the Counting Constraint Satisfaction Problem
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part I
Holographic Algorithms by Fibonacci Gates and Holographic Reductions for Hardness
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
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
The complexity of weighted Boolean #CSP with mixed signs
Theoretical Computer Science
The Complexity of Weighted Boolean CSP
SIAM Journal on Computing
On blockwise symmetric signatures for matchgates
Theoretical Computer Science
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
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Holographic reductions between some Holant problems and some #CSP(Hd) problems are built, where Hd is some complex value binary function. By the complexity of these Holant problems, for each integer d ≥ 2, #CSP(Hd) is in P when each variables appears at most d times, while it is #P-hard when each variables appears at most d + 1 times. #CSP(Hd) counts weighted summation of graph homomorphisms from input graph G to graph Hd, and the maximum occurrence of variables is the maximum degree of G. We conjecture the converse of holographic reduction holds for most of #Bi-restriction Constraint Satisfaction Problems, which can be regarded as a generalization of a known result about counting graph homomorphisms. It is proved that the converse of holographic reduction holds for some classes of problems.