Using flexibility in P-circuits by Boolean Relations

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.