Logic Synthesis for Generalization and Learning Addition

Abstract

Logic synthesis generates a logic circuit of a given Boolean function, where the size and depth of the circuit are optimized for small area and low delay. On the other hand, machine learning has been extensively studied and used for many applications these days. Its general approach of training a model from a set of input-output samples is similar to logic synthesis with external don t-cares, except that in the case of machine learning the goal is to come up with a general understanding from the given samples. Seeing this resemblance from another perspective, we can think of logic synthesis targeting a generalization of the care-set. In this paper, we try such logic synthesis that generates a logic circuit where the given incomplete relation between input and output is generalized. We compared popular logic synthesis methods and machine learning models and analyzed their characteristics. We found that there were some arithmetic functions that these conventional models cannot effectively learn. Out of them, we further experimented on addition operations using tree models and found a heuristic minimization method of BDD achieves the highest accuracy.