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 >>>

This paper proves the first super-logarithmic lower bounds on the cell probe complexity of dynamic \emph{boolean} (a.k.a. decision) data structure problems, a long-standing milestone in data structure lower bounds.

We introduce a new method for proving dynamic cell probe lower bounds and use it to prove a $\tilde{\Omega}(\log^{1.5} ... more >>>

Residuality plays an essential role for learning finite automata.
While residual deterministic and nondeterministic
automata have been understood quite well, fundamental
questions concerning alternating automata (AFA) remain open.
Recently, Angluin, Eisenstat, and Fisman have initiated
a systematic study of residual AFAs and proposed an algorithm called AL*
-an extension of ... more >>>