Algorithm for constructing minimal representations of multiple-output Boolean functions in the reversible logic circuits

Abstract

In this paper, we study the problem Boolean function's representation in a class of reversible circuits. Each Boolean function is associated with reversible function, which is implemented by a reversible circuit. Reversible circuits are built from Toffoli elements. An operator approach is used for description of this representation. At building of reversible circuit the algorithm of finding of the minimum representation of Boolean function in a class of the extended polarized Zhegalkin polynomials is applied. The foundation of this algorithm is made by a embedding of a special operator form (SOF) of function in certain classes of operators. Previously generated library with the components corresponding to certain operators is used at construction of a Boolean function's SOF. Operators of a SOF, and the corresponding multiple-output reversible function, define the minimal reversible circuit for a given Boolean function.