On Partial Differential Encodings, with Application to Boolean Circuits
share
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.
READ FULL TEXT