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- W3201455825 abstract "We prove a complexity dichotomy for a class of counting problems expressible as bipartite 3-regular Holant problems. For every problem of the form $operatorname{Holant}left(fmid =_3 right)$, where $f$ is any integer-valued ternary symmetric constraint function on Boolean variables, we prove that it is either P-time computable or #P-hard, depending on an explicit criterion of $f$. The constraint function can take both positive and negative values, allowing for cancellations. The dichotomy extends easily to rational valued functions of the same type. In addition, we discover a new phenomenon: there is a set $mathcal{F}$ with the property that for every $f in mathcal{F}$ the problem $operatorname{Holant}left(fmid =_3 right)$ is planar P-time computable but #P-hard in general, yet its planar tractability is by a combination of a holographic transformation by $left[begin{smallmatrix} 1 & 1 1 & -1 end{smallmatrix}right]$ to FKT together with an independent global argument." @default.
- W3201455825 created "2021-09-27" @default.
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- W3201455825 date "2021-01-01" @default.
- W3201455825 modified "2023-10-16" @default.
- W3201455825 title "Bipartite 3-Regular Counting Problems with Mixed Signs" @default.
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- W3201455825 doi "https://doi.org/10.1007/978-3-030-86593-1_9" @default.
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