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Complexitylib.Algebraic.LowerBound.KarchmerWigderson

Karchmer–Wigderson games and the KRW conjecture #

This umbrella collects De Morgan formulas, Karchmer–Wigderson protocols, the theorem identifying formula depth and size with protocol depth and size (for n ≥ 1 input bits), the composition of Boolean functions with its elementary bounds, the statement of the Karchmer–Raz–Wigderson conjecture, Khrapchenko's quadratic lower bounds for parity, threshold functions and majority, and their extension to circuits in which at most k gates have fan-out at least two, stated both for programs with k shared gates and for the library's De Morgan circuits, with a matching upper bound for parity, and the extension of these bounds to circuits that also have r binary XOR and EQUIV gates (Algebraic.KW.Extended).