Measuring Area-Complexity Using Boolean Difference

TLDR: This paper demonstrates how to capture the area-complexity of a Boolean function using the complexity of its Boolean derivatives using the theory of Boolean difference and Taylor expansion for Boolean functions.

Abstract: For a combinational circuit, area-complexity is a measure that estimates the logic area of the circuit without mapping to logic gates. Several measures like literal count, number of primary input/outputs, etc. have been used in the past as area-complexity metrics. In this paper, we propose a novel area-complexity measure using the theory of Boolean difference and Taylor expansion for Boolean functions. We demonstrate how to capture the area-complexity of a Boolean function using the complexity of its Boolean derivatives. We evaluate the metric on circuits from MCNC benchmark suite and a sizeable collection of randomly generated circuits. We compare our metric with existing techniques based on literal-count and BDD properties. We show that the new area-complexity measure is accurate within 10% of the actual number of gates synthesized using ABC as opposed to at least 100% and 15% for the metrics based on literal-count and BDD properties respectively. We also show the robustness of our metric across three different gate-libraries.