Minimisation algorithm for three-level mixed AND-OR-EXOR∕AND-OR-EXNOR representation of Boolean functions

Abstract

The AND-OR-EXOR form of a logic function comprises a pair of sum-of-products expressions (groups) connected by a single EXOR operator, such that the result realises the function. This paper presents several fast AND-OR-EXOR optimisation algorithms based on our previous technique for AND-OR-EXOR minimisation. It has been observed using benchmarks that this technique is able to produce results faster than our previous technique for most of the benchmarks without compromising the quality much. There are some functions which have a good AND-OR-EXOR representation, while there are others which have a good representation in the AND-OR-EXNOR or the mixed AND-OR-EXOR/AND-OR-EXNOR form. Keeping this in view a new heuristic minimisation algorithm for mixed AND-OR-EXOR/AND-OR-EXNOR forms is presented. A fast phase computation technique has been applied to several stages of the minimiser. The algorithm has been tested on many benchmarks and the results show that it is able to produce substantially better results for the majority of the benchmarks compared to any previously reported techniques. It has also been applied to adders and the results show that it is able to produce very good results for these.