Pavel Hrubes, Stasys Jukna, Alexander Kulikov, Pavel Pudlak

Khrapchenko's classical lower bound $n^2$ on the formula size of the

parity function~$f$ can be interpreted as designing a suitable

measure of subrectangles of the combinatorial rectangle

$f^{-1}(0)\times f^{-1}(1)$. Trying to generalize this approach we

arrived at the concept of \emph{convex measures}. We prove the

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Robert Robere, Jeroen Zuiddam

We study the amortized circuit complexity of boolean functions.

Given a circuit model $\mathcal{F}$ and a boolean function $f : \{0,1\}^n \rightarrow \{0,1\}$, the $\mathcal{F}$-amortized circuit complexity is defined to be the size of the smallest circuit that outputs $m$ copies of $f$ (evaluated on the same input), ...
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