Local holographic transformations: tractability and hardness

Peng YANG, Zhiguo FU

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Front. Comput. Sci. ›› 2023, Vol. 17 ›› Issue (2) : 172401. DOI: 10.1007/s11704-022-1231-5
RESEARCH ARTICLE

Local holographic transformations: tractability and hardness

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Abstract

Local holographic transformations were introduced by Cai et al., and local affine functions, an extra tractable class, were derived by it in #CSP2. In the present paper, we not only generalize local affine functions to #CSPd for general d, but also give new tractable classes by combining local holographic transformations with global holographic transformations. Moreover, we show how to use local holographic transformations to prove hardness. This is of independent interests in the complexity classification of counting problems.

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Keywords

#CSPd / Holant problems / local holographic transformations

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Peng YANG, Zhiguo FU. Local holographic transformations: tractability and hardness. Front. Comput. Sci., 2023, 17(2): 172401 https://doi.org/10.1007/s11704-022-1231-5

Peng Yang is currently a PhD student in the School of Information Science and Technology, Northeast Normal University, China. His currently research interests include computational complexity of counting problems

Zhiguo Fu received the PhD degree in the school of Mathematics from Jilin University, China. He is an associate professor and doctoral supervisor at Northeast Normal University, China. His research interests lie in theoretical computer science

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant No. 61872076) and the Natural Science Foundation of Jilin Province (20200201161JC).

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2023 Higher Education Press
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