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

The notion of switching activity is introduced for Boolean functions. It complements the previously studied static Activity, and models the power consumption associated with signal transition processes in integrated circuits.
An upper bound linear in $n$ for the Shannon function is obtained for the switching activity of Boolean functions of $n$ variables implemented by Boolean circuits in an arbitrary finite complete basis. Furthermore, methods for the synthesis of Boolean circuits are introduced, which make it possible to build Boolean circuits for arbitrary Boolean functions of $n$ variables with an asymptotically optimal complexity of ${2^n}/n$, the dynamic and static activities linear with respect to $n$, and the static activity meeting new, more accurate estimates.