Jan Johannsen

Using a notion of real communication complexity recently

introduced by J. Krajicek, we prove a lower bound on the depth of

monotone real circuits and the size of monotone real formulas for

st-connectivity. This implies a super-polynomial speed-up of dag-like

over tree-like Cutting Planes proofs.

Pavel Hrubes, Pavel Pudlak

We show that if a Boolean function $f:\{0,1\}^n\to \{0,1\}$ can be computed by a monotone real circuit of size $s$ using $k$-ary monotone gates then $f$ can be computed by a monotone real circuit of size $O(sn^{k-2})$ which uses unary or binary monotone gates only. This partially solves an open ... more >>>

Stasys Jukna, Andrzej Lingas

We consider Boolean circuits over $\{\lor,\land,\neg\}$ with negations applied only to input variables. To measure the ``amount of negation'' in such circuits, we introduce the concept of their ``negation width.'' In particular, a circuit computing a monotone Boolean function $f(x_1,\ldots,x_n)$ has negation width $w$ if no nonzero term produced (purely ... more >>>