An Algorithm for Identifying Symmetric Variables in the Canonical Reed–Muller Algebra System

Abstract

To simplify the process for identifying 12 types of symmetric variables in the canonical Reed–Muller (CRM) algebra system, we propose a new symmetry detection algorithm based on AND-XOR expansion. By analyzing the relationships between the coefficient matrices of sub-functions and the order coefficient subset matrices based on AND-XOR expansion around two arbitrary logical variables, the constraint conditions of the order coefficient subset matrices are revealed for 12 types of symmetric variables. Based on the proposed constraints, the algorithm is realized by judging the order characteristic square value matrices. The proposed method avoids the complicated process for separating the AND–XOR expansion coefficients into different groups in the Reed–Muller transform methods and solves the problem of completeness in the RM type decomposition map method. The application results show that, compared with traditional methods the new algorithm is an optimal detection method in terms of applicability of the number of logical variables, detection types, and complexity of the identification process. The algorithm has been implemented in C language and tested on MCNC91 benchmarks. Experimental results show that the proposed algorithm is convenient and efficient.