Restricted branching programs are considered by the investigation
of relationships between complexity classes of Boolean functions.
Read-once ordered branching programs (or OBDDs) form the most restricted class
of this computation model.
Since the problem of proving exponential lower bounds on the complexity
for general probabilistic OBDDs is open so ... more >>>

We extend Lutz's measure to probabilistic classes, and obtain notions of measure on probabilistic complexity classes
C
such as BPP , BPE and BPEXP. Unlike former attempts,
all our measure notions satisfy all three Lutz's measure axioms, that is
every singleton {L} has measure zero ... more >>>

A $c$-short program for a string $x$ is a description of $x$ of length at most $C(x) + c$, where $C(x)$ is the Kolmogorov complexity of $x$. We show that there exists a randomized algorithm that constructs a list of $n$ elements that contains a $O(\log n)$-short program for $x$. ... more >>>

We study the probabilistic degree over reals of the OR function on $n$ variables. For an error parameter $\epsilon$ in (0,1/3), the $\epsilon$-error probabilistic degree of any Boolean function $f$ over reals is the smallest non-negative integer $d$ such that the following holds: there exists a distribution $D$ of polynomials ... more >>>