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Matchgate Signatures Under Variable Permutations

Authors Boning Meng , Yicheng Pan

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LIPIcs.ISAAC.2025.50.pdf
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ACM Subject Classification
  • Theory of computation → Problems, reductions and completeness
Keywords
  • Computational Complexity
  • Matchgate Signature
  • Counting CSP

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Abstract

In this work, we introduce the concept of permutable matchgate signatures and leverage it to establish dichotomy theorems for #CSP and #R_D-CSP (D ≥ 3) on planar graphs without the variable ordering restriction. We also present a complete characterization of permutable matchgate signatures and their relationship to symmetric signatures. Besides, we give a sufficient and necessary condition for determining whether a matchgate signature retains its property under a certain variable permutation, which can be checked in polynomial time. In addition, we prove a dichotomy for Pl-#R_D-CSP (D ≥ 3), where the variable ordering restriction exists.

Cite As Get BibTex

Boning Meng and Yicheng Pan. Matchgate Signatures Under Variable Permutations. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 50:1-50:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.ISAAC.2025.50

Author Details

Boning Meng
  • Key Laboratory of System Software (Chinese Academy of Sciences) and State Key Laboratory of Computer Science, Institute of Software, Chinese Academy of Sciences, Beijing, China
  • University of Chinese Academy of Sciences, Beijing, China
Yicheng Pan
  • State Key Laboratory of Complex & Critical Software Environment, Beihang University, Beijing, China

Funding

  • Meng, Boning: supported by National Key R&D Program of China (2023YFA1009500), NSFC 62532014 and NSFC 62272448.
  • Pan, Yicheng: supported by State Key Laboratory of Complex & Critical Software Environment (SKLCCSE-2024ZX-20) and NSFC 61932002.

Acknowledgements

We want to thank Mingji Xia for introducing this problem to us.

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