Exclusive or Sum of Complex Terms expressions minimization

Abstract

This paper demonstrates both theoretically, through theorem proofs, and experimentally, that existing minimization algorithms for ESOP (Exclusive or Sum Of Products) expressions can be successfully used for minimizing ESCT (Exclusive or Sum of Complex Terms) expressions as well. ESCT expressions are more general than ESOP ones and being reversible are very useful for logic design and for quantum circuits. The field of ESOP minimization has received considerable attention along the years and a great number of research works can be found in the literature, in contrast to the ESCT minimization problem with much fewer works addressing it. The open problems of finding exact ESCT expressions for completely specified functions of more than six variables as well as the problem of finding exact ESCT expressions for incompletely specified functions are solved here based on ESOP principles, for the first time.