Synthesis of P-circuits for logic restructuring

Minimization of P-Circuits Using Boolean Relations

“…In fact, P circuits synthesized with Boolean relations (P-circuit fJL and P-circuit fJBDD) turned out to be more compact than the corresponding P-circuits proposed in [3] in about 92% and 78% of our experiments, respectively. In fact, P circuits synthesized with Boolean relations (P-circuit fJL and P-circuit fJBDD) turned out to be more compact than the corresponding P-circuits proposed in [3] in about 92% and 78% of our experiments, respectively.…”

“…To evaluate the obtained circuits, we ran them using the SIS system with the MCNC library for technology mapping and the SIS cOlmnand map -W -f 3 -S o To show the gain in area of P-circuits derived using Boolean relations, we compare our results with the algorithm based on don't cares reported in [3]. To highlight the importance of projecting the intersection, we report also the results regarding circuits decomposed with standard Shannon decomposition (therefore without any intersection), called here S-circuits.…”

“…In this section we first briefly review the P-circuits based on SOP minimization [1], [2], [3]. In this section we first briefly review the P-circuits based on SOP minimization [1], [2], [3].…”

“…To favor area minimiza tion while pushing signals ahead in the circuit, extended forms of Shannon cofactoring, P-circuits, were investigated in [1], [2], [3], where the expansion is with respect to an orthogonal basis Xi EEl p (i.e., Xi = p), and Xi EEl p (i.e., Xi i=p), where p is a function defined over all variables except the critical variable Xi. To favor area minimiza tion while pushing signals ahead in the circuit, extended forms of Shannon cofactoring, P-circuits, were investigated in [1], [2], [3], where the expansion is with respect to an orthogonal basis Xi EEl p (i.e., Xi = p), and Xi EEl p (i.e., Xi i=p), where p is a function defined over all variables except the critical variable Xi.…”

“…The computation of the complete flexibility of P-circuits has been already described in the literature [1], [2], [3], but the algorithms proposed so far for its exploitation may fail to find the best implementation, because they cast the optimization problem as the minimization of an incompletely specified function. Instead, in this paper we show that to explore all solutions we must set up the problem as the minimization of a Boolean relation, because there are combinations of don't care conditions that cannot be expressed by single cubes.…”