On the complexity of H-coloring
Journal of Combinatorial Theory Series B
Complexity theory of real functions
Complexity theory of real functions
Finite fields
Complexity and real computation
Complexity and real computation
The complexity of counting graph homomorphisms
Proceedings of the ninth international conference on on Random structures and algorithms
Complexity classifications of boolean constraint satisfaction problems
Complexity classifications of boolean constraint satisfaction problems
The complexity of satisfiability problems
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
The complexity of partition functions
Theoretical Computer Science - Automata, languages and programming: Algorithms and complexity (ICALP-A 2004)
The rank of connection matrices and the dimension of graph algebras
European Journal of Combinatorics
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
Holant problems and counting CSP
Proceedings of the forty-first annual ACM symposium on Theory of computing
FAW'10 Proceedings of the 4th international conference on Frontiers in algorithmics
A Complexity Dichotomy for Partition Functions with Mixed Signs
SIAM Journal on Computing
A computational proof of complexity of some restricted counting problems
Theoretical Computer Science
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
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
Approximate counting via correlation decay in spin systems
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
The complexity of weighted and unweighted #CSP
Journal of Computer and System Sciences
Dichotomy for Holant problems of Boolean domain
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Complexity of counting CSP with complex weights
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Spin systems on k-regular graphs with complex edge functions
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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Graph homomorphism problem has been studied intensively. Given an m × m symmetric matrix A, the graph homomorphism function ZA(G) is defined as ZA(G) = σξ:V →[m] (u,v)∈E ΠAξ(u),ξ(v), where G = (V,E) is any undirected graph. The function ZA(G) can encode many interesting graph properties, including counting vertex covers and k-colorings. We study the computational complexity of ZA(G), for arbitrary complex valued symmetric matrices A. Building on the work by Dyer and Greenhill [1], Bulatov and Grohe [2], and especially the recent beautiful work by Goldberg, Grohe, Jerrum and Thurley [3], we prove a complete dichotomy theorem for this problem.