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Also, classifying all Holant problems for general asymmetric complex-weighted signatures remains elusive. Partial results have been obtained for Holantc problems[2]orHolantproblemswithnon-negativelyweightedsignatures[36]. 2 Preliminaries Problems and Definitions The framework of Holant problems is defined for functions mapping any[q]n! R. Svenska konstnärer tavlor
A Complete Dichotomy Rises from the Capture of Vanishing Signatures Jin-Yi Cai University of Wisconsin-Madison jyc@ Heng Guo University of Wisconsin-Madison hguo@ Svensk konstnär 3 bokstäver
some progress for Holant problems [5], classifying Holant problems on regular bipartite graphs is particularly challenging. In a very recent paper[15] we initiated the study of Holant problems on the simplest setting of 3-regular bipartite graphs with nonnegative constraint functions. Admittedly. Finska nutida konstnärer
Jin-Yi Caiy Abstract We prove a complexity dichotomy theorem for the following class of Holant Problems. Given a 3-regular graph G = (V; E), compute Holant(G) = Y g(f3⁄4(u); 3⁄4(v)g);:V!f0;1g fu;vg2E where the (symmetric) edge function g is arbitrary complex valued. Konstnär r
Shuai Shao Department of Computer Sciences, University of Wisconsin-Madison, Madison, WI, USA sh@ Abstract Holant problems are intimately connected with quantum theory as tensor networks. We first use techniques from Holant theory to derive new and improved results for quantum entanglement theory. Konstnär ae
Three new techniques are introduced: (1) higher dimensional iterations in interpolation; (2) Eigenvalue Shifted Pairs, which allow us to prove that a pair of combinatorial gadgets in combination succeed in proving #P-hardness; and (3) algebraic symmetrization, which significantly lowers the symbolic complexity of the proof for computational comp. Identifiera konstnär signatur
Holant problems are a family of counting problems parameterized by sets of algebraic-complex-valued constraint functions and defined on graphs. They arise from the theory of holographic algorithms, which was originally inspired by concepts from quantum computation.
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A very broad subclass of Holant problems is called Holantc, where only two unary pinning functions 0, 1 (that set a variable to 0 or 1) are assumed to be available. Holantcalready covers a lot of ground, including all of #CSP, graph matching and so on. #CSP is the special case of Holant problems where the constraint function set is assumed to.