Holant Problems for Regular Graphs with Complex Edge Functions release_tiptkoiuqndjbat5wx4tjcf75m

by Michael Kowalczyk, Jin-Yi Cai

Released as a article .

2010  

Abstract

We prove a complexity dichotomy theorem for Holant Problems on 3-regular graphs with an arbitrary complex-valued edge function. 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 complexity. With holographic reductions the classification theorem also applies to problems beyond the basic model.
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Date   2010-01-04
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arXiv  1001.0464v1
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