A compact factored form for a Boolean function

A factored form of a Boolean function is a common representation to express the complexity of a Boolean function in multi-level logic. However, a factored form which inhibits the appearance of the inversion operation is still a restricted way of representing a multi-level circuit. In this paper, we present a novel representation of a Boolean function, called the invert factored form representation. This representation mainly takes advantage of the inversion of whole or part of a Boolean function so that fewer literals and better multi-level circuit implementation can be obtained. Based on this novel presentation, our algorithm attempts to find a minimal expression. Experimental results also show the literal counts based on the novel representation are smaller than those on the traditional factored form representation.