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arXiv · 2307.16078

Restricted Holant Dichotomy on Domains 3 and 4

Yin Liu·Austen Z. Fan·Jin-Yi Cai
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Abstract

$\operatorname{Holant}^*(f)$ denotes a class of counting problems specified by a constraint function $f$. We prove complexity dichotomy theorems for $\operatorname{Holant}^*(f)$ in two settings: (1) $f$ is any arity-3 real-valued function on input of domain size 3. (2) $f$ is any arity-3 $\{0,1\}$-valued function on input of domain size 4.

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Yin Liu, Austen Z. Fan, Jin-Yi Cai. 2023-07-29. Restricted Holant Dichotomy on Domains 3 and 4. https://arxiv.org/abs/2307.16078

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