Minimization of logic functions is very important for the development of simpler, smaller and faster integrated circuits which are used in almost every area of IT sector. Many techniques and algorithms have been developed to simplify logic functions. In this study, a new version of direct cover technique is presented. In addition, minimization process is improved by finding isolated minterms in logic function files. Algorithms for presented minimization technique are prepared and parallel computing algorithms compatible with multicore computers are developed and all these algorithms are coded in Microsoft C# program.

The following questions have been answered in this study; how much minimization is possible for logic function files, how the process of finding isolated minterms affect function minimization, what is the potential speedup in parallelization of function minimization and isolated minterm detection algorithms. Results revealed that minimization ratio of Close Results Covering Algorithm (Yakın Sonuç Kapsama Algoritması, YSKA) (82.86%) are increased by 0.34% in Exact Results Covering Algorithm (Kesin Sonuç Kapsama Algoritması, KSKA) algorithm (83.20%). Both YSKA and KSKA finds equal number of PIs in 41 benchmarks and KSKA finds better results in 9 benchmarks. However, YSKA computes PIs 6.92 times faster. It was also found that YSKA and KSKA perform the same or very close minimization results in benchmarks where input variable and ON minterms are not high. On benchmarks with a high number of ON and/or OFF minterms, KSKA achieved better results despite its high uptime.

In this thesis, it has been found that the detection of isolated minterms improves the quality of the results of both YSKA and KSKA and decreases the average computing time. The detection algorithm of isolated minterms resulted in 2.33% quality increase and 12.68% faster computing time on YSKA. The detection algorithm of isolated minterms resulted in 1.09% quality increase and 6.51% faster computing time on KSKA. While the algorithm developed for detecting and sorting the isolated minterm uses processing time in the sorting phase, it saves time in minimization phase by facilitating the work of the YSKA and KSKA.

While parallelization of algorithms has provided significant improvements in detection of isolated minterms and YSKA (49.37%, 22.88%), there was no significant improvement (1.18%, 0.65%) in KSKA algorithm. Parallel programming had no effect on the result quality of the algorithms like the number of prime implicants.