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Holant Problems for Regular Graphs with Complex Edge Functions
release_tiptkoiuqndjbat5wx4tjcf75m
by
Michael Kowalczyk, Jin-Yi Cai
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.
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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1001.0464v1
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