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Holant Problems for Regular Graphs with Complex Edge Functions

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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Submitted on : Thursday, February 11, 2010 - 10:09:31 AM
Last modification on : Wednesday, August 7, 2019 - 2:12:02 PM
Long-term archiving on: : Friday, June 18, 2010 - 6:21:07 PM


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  • HAL Id : inria-00455751, version 1



Michael Kowalczyk, Jin-Yi Cai. Holant Problems for Regular Graphs with Complex Edge Functions. 27th International Symposium on Theoretical Aspects of Computer Science - STACS 2010, Inria Nancy Grand Est & Loria, Mar 2010, Nancy, France. pp.525-536. ⟨inria-00455751⟩



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