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On Partial Differential Encodings, with Application to Boolean Circuits

08/15/2020

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by Edinah K. Gnang, et al.

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The present work argues that strong arithmetic circuit lower bounds yield Boolean circuit lower bounds. In particular we show that the De Morgan Boolean formula complexity upper-bounds algebraic variants of the Kolomogorov complexity measure of partial differential incarnations of Turing machines. We devise from this connection new non-trivial upper and lower bounds for the De Morgan Boolean formula complexity of some familiar Boolean functions.

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