The computational complexity of Holant problems on 3-regular graphs

被引：0
|
作者：
Yang, Peng [1 ,2 ]
Huang, Yuan [1 ,2 ]
Fu, Zhiguo [1 ,2 ]
机构：
[1] Northeast Normal Univ, Sch Informat Sci & Technol, Changchun 130117, Peoples R China
[2] Northeast Normal Univ, KLAS, Changchun 130117, Peoples R China
来源：
THEORETICAL COMPUTER SCIENCE | 2024年 / 982卷
基金：
中国国家自然科学基金;
关键词：
Holant problems; Computational complexity; Dichotomy; SLOCC; HOLOGRAPHIC ALGORITHMS; DICHOTOMY;
D O I：
10.1016/j.tcs.2023.114256
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
Holant problem is a framework to study counting problems, which is expressive enough to contain Counting Graph Homomorphisms (#GH) and Counting Constraint Satisfaction Problems (#CSP) as special cases. In the present paper, we classify the computational complexity of Holant problems on 3-regular graphs, where the signature is complex valued and not necessarily symmetric. In details, we prove that Holant problem on 3-regular graphs is #P-hard except for the signature is not genuinely entangled, A-transformable, P-transformable or vanishing, in which cases the problem is tractable.
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页数：13
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