Complexity of representations of multiple-output Boolean functions in the reversible logic circuits

In this paper, we study the problem of finding the complexity of representations of Boolean functions in classes of polynomials and reversible circuits of a special form. The extending Zhegalkin basis (Reed-Muller) is used as a basis of polynomials. Reversible circuits are constructed from elements of Toffoli basis. Each Boolean function is associated with reversible function, which is implemented by a reversible circuit. Reversible circuits are constructed for representation of Boolean function in the extended Reed-Muller form. An operator approach is used for description of this representation. An exact value of the complexity of reversible circuits representing multiple-output Boolean functions in Toffoli basis was found and synthesis method for these circuits has been proposed.