Abstract
We introduce the method of proving complexity dichotomy theorems by holographic reductions. Combined with interpolation, we present a unified strategy to prove #P-hardness. Specifically, we prove a complexity dichotomy theorem for a class of counting problems on 2–3 regular graphs expressible by Boolean signatures. For these problems, whenever a holographic reduction followed by interpolation fails to prove #P-hardness, we can show that the problem is solvable in polynomial time.
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Cai, JY., Lu, P. & Xia, M. Holographic reduction, interpolation and hardness. comput. complex. 21, 573–604 (2012). https://doi.org/10.1007/s00037-012-0044-6
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DOI: https://doi.org/10.1007/s00037-012-0044-6