# Measuring Area-Complexity Using Boolean Difference

TL;DR: 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.

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229,202 citations

### "Measuring Area-Complexity Using Boo..." refers methods in this paper

...We use R Statistical Computing Tool [13], to perform linear regression....

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737 citations

### "Measuring Area-Complexity Using Boo..." refers background in this paper

...The area-complexity of a circuit can be measured in terms of the number of inputs or literals or gates, etc. Characterizing logic functions and estimation of areacomplexity dates back to 1949 when Shannon [1] measured the area-complexity as the amount of switching activity in the circuit....

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...We exploit this relationship and propose a metric for estimating the number of logic gates required by a function....

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197 citations

### "Measuring Area-Complexity Using Boo..." refers background in this paper

...For a Boolean function F (x1, x2, ..., xn), the cofactor of F (Fa) w.r.to a literal a = xi or a = x̄i is defined as Fxi(x1, ..., xi, ..., xn) = F (x1, ..., 1, ..., xn) Fx̄i(x1, ..., xi, ..., xn) = F (x1, ..., 0, ..., xn) Fxi and Fx̄i are called the positive cofactor and the negative cofactor of F…...

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...1 and 2 are called as the 1-fold and the 2-fold Boolean derivatives of F respectively....

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124 citations

### "Measuring Area-Complexity Using Boo..." refers methods in this paper

...With rising popularity of BDDs in the 1990’s, many metrics used the structural parameters of the BDDs, like the number of nodes, as an area-complexity measure [7], [8]....

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117 citations

### "Measuring Area-Complexity Using Boo..." refers background in this paper

...This can lead to overprediction of the number of gates as frequent application of logic synthesis algorithms often reduces the gate-count....

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