An $r$-simple $k$-path is a {path} in the graph of length $k$ that
passes through each vertex at most $r$ times. The \simpath{r}{k}
problem, given a graph $G$ as input, asks whether there exists an
$r$-simple $k$-path in $G$. We first show that this problem is
NP-Complete. We then show ... more >>>

We study the proper learnability of axis parallel concept classes
in the PAC learning model and in the exact learning model with
membership and equivalence queries. These classes include union of boxes,
DNF, decision trees and multivariate polynomials.

For the {\it constant} dimensional axis parallel concepts $C$
we ... more >>>

We study attribute efficient learning in the PAC learning model with
membership queries. First, we give an {\it attribute efficient}
PAC-learning algorithm for DNF with membership queries under the
uniform distribution. Previous algorithms for DNF have sample size
polynomial in the number of attributes $n$. Our algorithm is the
first ... more >>>

We present a new approach to the composition
of learning algorithms (in various models) for
classes of constant VC-dimension into learning algorithms for
more complicated classes.
We prove that if a class $\CC$ is learnable
in time $t$ from a hypothesis class $\HH$ of constant VC-dimension
then the class ... more >>>

This paper solves the open problem of exact learning
geometric objects bounded by hyperplanes (and more generally by any constant
degree algebraic surfaces) in the constant
dimensional space from equivalence queries only (i.e., in the on-line learning
model).

We present a novel approach that allows, under ... more >>>

This paper studies the learnability of branching programs and small depth
circuits with modular and threshold gates in both the exact and PAC learning
models with and without membership queries. Some of the results extend earlier
works in [GG95,ERR95,BTW95]. The main results are as follows. For
branching programs we ... more >>>

We present a $2^{\tilde O(\sqrt{n})}$ time exact learning
algorithm for polynomial size
DNF using equivalence queries only. In particular, DNF
is PAC-learnable in subexponential time under any distribution.
This is the first subexponential time
PAC-learning algorithm for DNF under any distribution.

We show that a DNF formula that has a CNF representation that contains
at least one ``$1/poly$-heavy''
clause with respect to a distribution $D$ is weakly learnable
under this distribution. So DNF that are not weakly
learnable under the distribution $D$ do not have
any ``$1/poly$-heavy'' clauses in any of ... more >>>