Minimization for ternary fixed polarity Reed–Muller expressions based on ternary quantum shuffled frog leaping algorithm

• Published in: Applied soft computing Vol. 110; p. 107647
• Main Authors: He, Zhenxue, Xiao, Limin, Wang, Xiang
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.10.2021
• Subjects: Combinational logic synthesis; Combinatorial optimization problem; Fixed polarity Reed–Muller; Logic minimization; Shuffled frog leaping algorithm; Combinational logic synthesis; Shuffled frog leaping algorithm; Fixed polarity Reed–Muller; Logic minimization; Combinatorial optimization problem
• ISSN: 1568-4946; 1872-9681
• DOI: 10.1016/j.asoc.2021.107647

Logic minimization is one of the most crucial steps in combinational logic synthesis. The minimization for ternary fixed polarity Reed–Muller (FPRM) expressions aims to find a polarity that produces a ternary FPRM expression with as few operation terms as possible. However, the size of the ternary FPRM optimization space is much larger than that of binary FPRM optimization space, and the minimization for ternary FPRM expressions is a computationally hard problem. In this paper, we first propose a ternary quantum shuffled frog leaping algorithm (TQSFL) to solve the three-valued combinatorial optimization problem. The TQSFL divides frog individuals into three subpopulations: a subpopulation with a global updating strategy, a subpopulation with a local updating strategy, and a subpopulation with a random updating strategy, and performs local depth search on the three subpopulations based on the proposed ternary quantum rotation gate, ternary quantum correction mechanism, and ternary quantum crossover operator. Moreover, based on the TQSFL, we propose a minimization algorithm (MA) for ternary FPRM expressions, which searches for a polarity that produces a ternary FPRM expression with as few operation terms as possible by using the TQSFL. Experimental results demonstrated the effectiveness of the MA in minimizing ternary FPRM expressions. •A ternary quantum rotation gate (TQRG) is proposed to update and optimize the worst frog encoded by qutrits.•A ternary quantum correction mechanism (TQCM) is proposed to jump out local optimum and accelerate the convergence speed.•A ternary quantum crossover operator (TQCO) is proposed to exchange gene information with multiple individuals.•A ternary quantum shuffled frog leaping algorithm (TQSFL) is proposed to solve the three-valued combinatorial optimization problem.•A minimization algorithm is proposed to minimize the ternary FPRM expressions by using the TQSFL.