Extending symmetric variable-pair transitivities using state-space transformations

Abstract

Detecting the symmetries of a Boolean function can lead to simpler implementations both at the hardware and software level. Large clusters of mutually symmetric variables are more advantageous than small clusters. One way to extend the symmetry of a function is to detect abstract two-cofactor relations in addition to ordinary symmetric relations. Unfortunately, ordinary symmetries are simply transitive but more complex types of relations are not. This paper shows how to convert the more complex relations into ordinary symmetries, allowing them to be used to form large clusters of symmetric variables, larger than would be possible using ordinary symmetries.