Using Flexibility in P-Circuits by Boolean Relations

Abstract

In this paper we study the problem of characterizing and exploiting the complete flexibility of a special logic architecture, called P-circuits, which realize a Boolean function by projecting it onto overlapping subsets given by a generalized Shannon decomposition. P-circuits are used to restructure logic by pushing some signals towards the outputs. The algorithms proposed so far for exploiting the structural flexibility of P-circuits do not guarantee to find the best implementation, because they cast the problem as the minimization of an incompletely specified function . Instead, here we show that to explore all solutions we must set up the problem as the minimization of a Boolean relation , because there are don’t care conditions that cannot be expressed by single cubes. Finally we report the results obtained using a minimizer of Boolean relations, which improve in a major way with respect to the previous literature.