Probabilistic characterization of controllability in general homogeneous circuits

Abstract A probabilistic model for the controllabilities of gates in different levels of reconvergence-free nand -gate circuits is formulated. Analytical relationships between the structural parameters (fanins) of a circuit and gate controllabilities are derived. This is achieved by characterizing the fanins of gates in a circuit using two parameters of a generalized geometric distribution. This statistical model for fanins is verified using data from well known benchmark circuits. It is shown that the behaviour of the controllabilities of gates depends on the values of the parameters of fanin distribution and the primary input controllability. Limiting values of expected controllability and rates of convergence to these limits under different conditions are presented. Further, conditions under which these results are applicable to general nand circuits (with reconvergent fanouts) are obtained. These results are extended to other homogeneous ( and, or and nor ) circuits.