Multiple-valued logic minimization by genetic algorithms

This paper describes an approach to minimize multiple-valued logic expressions by genetic algorithms. We encode a multiple-valued logic expression as a ''chromosome'' whose length allows to change and corresponds to the number of implicants of the expression. Our fitness function evaluates the following three items. 1. How may outputs does the logic expression represent correctly? 2. How many implicants does the logic expression require? 3. How many connections does the logic expression require? Our method employs the fitness function and minimizes sum-of-products expressions, where sum refers to TSUM or MAX and product refers to MIN of set literals or window literals. The simulation results show that our method derives good results for some arithmetic functions and intends to avoid the local minimal solution, compared to neural-computing-based method.