On Deducing the Clique Potential of Nanoscale Combinational Circuits

In the backdrop of probabilistic computing defining the landscape of nanoscale digital logic circuits, a combinational circuit is usually specified in terms of a set of fully connected variable nodes called the ‘clique’. The clique energy or clique potential is an indicator of correct circuit operation under the premise of non-deterministic nature of device parameters at nanoscale dimensions. Also, the clique potential forms an important parameter in the probabilistic analysis of digital circuits with respect to the Markov random field model as well as in computing the probability density function. The major problem inherent in determining the clique energy expression of an arbitrary logic function that features multiple inputs and outputs is the computational complexity. The number of primary inputs and outputs governs the order of the clique potential, and hence an explosion of input and output state spaces is imminent. In this context, this paper presents a novel scheme of deriving the clique expression by segregating the primary outputs and operating upon them in parallel, thus restraining the state space expansion significantly by O(2n-1) where n signifies the number of primary outputs of the combinational logic. The important result shown in this work is that the clique potential of an arbitrary combinational circuit is equal to the Boolean product of clique potentials of its primary outputs.