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Abstract
The classification of Boolean functions plays an underpinning role in logic design and synthesis of VLSI circuits. This paper considers a underpinning question in Boolean function classification: how many distinct classes are there for k-input Boolean functions. We exploit various group algebraic properties to efficiently compute the number of unique equivalent classes. We have reduced the computation complexity from 2mm! to (m + 1)!. We present our analysis for NPN classification of Boolean functions with up to ten variables and compute the number of NP and NPN equivalence classes for 3-10 variables. This is the first time to report the number of NP and NPN classifications for Boolean functions with 9-10 variables. We demonstrate the effectiveness of our method by both theoretical proofs and numeric experiments.
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