Analysis of direct cover algorithms for minimization of MVL functions

There exist a number of algorithms for minimization of MVL functions. The main objective is to produce near minimal expressions for MVL functions at an affordable cost (measured in terms of CPU time). Among the proposed heuristic-based techniques, direct cover-based techniques have received the most attention. In this paper, we analyze two of the existing direct cover techniques in terms of the number of implicants needed to synthesize a given function. We introduce five modified techniques and analyze them as well. An overall comparison is conducted among the existing and the proposed techniques. The analysis is based on performance measures of these techniques for 50,000 2-variable 4-valued and 21,000 2-variable 5-valued randomly selected functions. The analysis shows that algorithm DM_MIN-2 outperforms all other considered algorithms. The algorithm introduced by Besslich is outperformed by all considered algorithms.