Let $X$ be a set of items of size $n$ , which may contain some defective items denoted by $I$, where $I \subseteq X$. In group testing, a {\it test} refers to a subset of items $Q \subset X$. The test outcome is $1$ (positive) if $Q$ contains at least ... more >>>

Koch, Strassle, and Tan [SODA 2023], show that, under the randomized exponential time hypothesis, there is no distribution-free PAC-learning algorithm that runs in time $n^{\tilde O(\log\log s)}$ for the classes of $n$-variable size-$s$ DNF, size-$s$ Decision Tree, and $\log s$-Junta by DNF (that returns a DNF hypothesis). Assuming a natural ... more >>>

We study the query complexity of one-sided $\epsilon$-testing the class of Boolean functions $f:F^n\to \{0,1\}$ that describe affine subspaces and Boolean functions that describe axis-parallel affine subspaces, where $F$ is any finite field. We give a polynomial-time $\epsilon$-testers that ask $\tilde O(1/\epsilon)$ queries. This improves the query complexity $\tilde O(|F|/\epsilon)$ ... more >>>

We give the first polynomial-time *non-adaptive* proper learning algorithm of Boolean sparse multivariate polynomial under the uniform distribution. Our algorithm, for $s$-sparse polynomial over $n$ variables, makes $q=(s/\epsilon)^{\gamma(s,\epsilon)}\log n$ queries where $2.66\le \gamma(s,\epsilon)\le 6.922$ and runs in $\tilde O(n)\cdot poly(s,1/\epsilon)$ time. We also show that for any $\epsilon=1/s^{O(1)}$ any non-adaptive ... more >>>

In this note we show that all sets that are neither finite nor too dense are non-trivial to test in the sense that, for every $\epsilon>0$, distinguishing between strings in the set and strings that are $\epsilon$-far from the set requires $\Omega(1/\epsilon)$ queries.
Specifically, we show that if, for ... more >>>

A Boolean function $f:\{0,1\}^n\to \{0,1\}$ is $k$-linear if it returns the sum (over the binary field $F_2$) of $k$ coordinates of the input. In this paper, we study property testing of the classes $k$-Linear, the class of all $k$-linear functions, and $k$-Linear$^*$, the class $\cup_{j=0}^kj$-Linear.
We give a non-adaptive distribution-free ... more >>>

We give improved and almost optimal testers for several classes of Boolean functions on $n$ inputs that have concise representation in the uniform and distribution-free model. Classes, such as $k$-Junta, $k$-Linear Function, $s$-Term DNF, $s$-Term Monotone DNF, $r$-DNF, Decision List, $r$-Decision List, size-$s$ Decision Tree, size-$s$ Boolean Formula, size-$s$ Branching ... more >>>

We prove that for every prime $p$ there exists a $(0,1)$-matrix
$M$ of size $t_p(n,m)\times n$ where
$$t_p(n,m)=O\left(m+\frac{m\log \frac{n}{m}}{\log \min({m,p})}\right)$$ such that every
$m$ columns of $M$ are linearly independent over $\Z_p$, the field
of integers modulo $p$ (and therefore over any field of
characteristic $p$ and over the real ... more >>>