Heuristic AND-OR-EXOR three-level minimisation algorithm for multiple-output incompletely-specified Boolean functions

Abstract

Given a logic function f, an AND-OR-EXOR representation of f comprises a pair of sum-of-products expressions connected by a single two-input EXOR operator such that the resulting expression realises f: The AND-OR-EXOR form of a logic function has been observed to have a more compact representation for functions like arithmetic, control, ALU circuits, etc. Compared to sum-of-products as well as EXOR-sum-of-products based representations. The problem of AND-OR-EXOR minimisation of logic functions is to find a suitable pair of sum-of-products expressions which will reduce the size of the representation and hence the resulting hardware. A new heuristic AND-OR-EXOR minimisation algorithm for multiple-output incompletely-specified logic functions has been developed. The algorithm is divided into two parts. The first part constitutes a new heuristic algorithm for decomposition of multiple-output incompletely specified logic functions for AND-OR-EXOR minimisation. The second part constitutes ANDOR-EXOR optimisation algorithms for multiple-output incompletely-specified logic functions. Using benchmark PLAs the authors show that their new AND-OR-EXOR minimisation algorithm is able to find better solutions than previous techniques.