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The complexity of graph homomorphism problems has been the subject of intense study for some years. In this paper, we prove a decidable complexity dichotomy theorem for the partition function of directed graph homomorphisms. Our theorem applies to all non-negative weighted forms of the problem: given any fixed matrix A with non-negative algebraic entries, the partition function ZA(G) of directed graph...
We explore the intricate interdependent relationship among counting problems, considered from three frameworks for such problems: Holant Problems, counting CSP and weighted H-colorings. We consider these problems for general complex valued functions that take boolean inputs. We show that results from one framework can be used to derive results in another, and this happens in both directions. Holographic...
The complexity of graph homomorphism problems has been the subject of intense study. It is a long standing open problem to give a (decidable) complexity dichotomy theorem for the partition function of directed graph homomorphisms. In this paper, we prove a decidable complexity dichotomy theorem for this problem and our theorem applies to all non-negative weighted form of the problem: given any fixed...
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