Switching activity of Boolean circuits and synthesis of Boolean circuits with asymptotically optimal complexity and linear switching activity

Abstract

For circuits of functional elements (CFEs), the concept of their switching activity is introduced, which complements the earlier analyzed static activity, or power, and models the power consumption of integrated circuits due to arising transient processes in them. For the switching activity of Boolean functions (BFs) of n variables realized by CFEs, a linear (in n) upper estimate for the Shannon function is obtained in an arbitrary finite complete basis. In addition, synthesismethods are proposed that allow one to construct such CFEs for the above functions in the standard basis {&, ∨, ¬}, whose complexity is asymptotically not greater than 2 n /n and the switching and static activities have a growth order linear with respect to n; moreover, the static activity of these CFEs satisfies new sharper estimates.