Related papers: Hard properties with (very) short PCPPs and their …
We study the Equitable Connected Partition (ECP for short) problem, where we are given a graph G=(V,E) together with an integer p, and our goal is to find a partition of V into p parts such that each part induces a connected sub-graph of G…
We study the role of perfect completeness in probabilistically checkable proof systems (PCPs) and give a new way to transform a PCP with imperfect completeness to a PCP with perfect completeness when the initial gap is a constant. In…
We prove that many of the results of the LMMP hold for $3$-folds over fields of characteristic $p>5$ which are not necessarily perfect. In particular, the existence of flips, the cone theorem, the contraction theorem for birational extremal…
Property Testing is a formal framework to study the computational power and complexity of sampling from combinatorial objects. A central goal in standard graph property testing is to understand which graph properties are testable with…
We initiate the systematic study of QMA algorithms in the setting of property testing, to which we refer as QMA proofs of proximity (QMAPs). These are quantum query algorithms that receive explicit access to a sublinear-size untrusted proof…
We characterize the set of properties of Boolean-valued functions on a finite domain $\mathcal{X}$ that are testable with a constant number of samples. Specifically, we show that a property $\mathcal{P}$ is testable with a constant number…
Suppose $G$ is a graph with degrees bounded by $d$, and one needs to remove more than $\epsilon n$ of its edges in order to make it planar. We show that in this case the statistics of local neighborhoods around vertices of $G$ is far from…
Given a $k$-uniform hyper-graph, the E$k$-Vertex-Cover problem is to find the smallest subset of vertices that intersects every hyper-edge. We present a new multilayered PCP construction that extends the Raz verifier. This enables us to…
We establish new upper and lower bounds on the number of queries required to test convexity of functions over various discrete domains. 1. We provide a simplified version of the non-adaptive convexity tester on the line. We re-prove the…
Energy-based learning algorithms, such as predictive coding (PC), have garnered significant attention in the machine learning community due to their theoretical properties, such as local operations and biologically plausible mechanisms for…
A PCP is a proof system for NP in which the proof can be checked by a probabilistic verifier. The verifier is only allowed to read a very small portion of the proof, and in return is allowed to err with some bounded probability. The…
Determinantal point processes (DPPs) are popular probabilistic models of diversity. In this paper, we investigate DPPs from a new perspective: property testing of distributions. Given sample access to an unknown distribution $q$ over the…
Invariance with respect to linear or affine transformations of the domain is arguably the most common symmetry exhibited by natural algebraic properties. In this work, we show that any low complexity affine-invariant property of…
We establish new exponential in dimension lower bounds for the Maximum Halfspace Discrepancy problem, which models linear classification. Both are fundamental problems in computational geometry and machine learning in their exact and…
A natural criticism of the optimal protocol of the irreversible work found for weakly driven processes is its experimental difficulty in being implementable due to its singular part. In this work, I explore the possibility of taking its…
We consider the problem of closeness testing for two discrete distributions in the practically relevant setting of \emph{unequal} sized samples drawn from each of them. Specifically, given a target error parameter $\varepsilon > 0$, $m_1$…
We construct near-optimal coresets for kernel density estimates for points in $\mathbb{R}^d$ when the kernel is positive definite. Specifically we show a polynomial time construction for a coreset of size $O(\sqrt{d}/\varepsilon\cdot…
The Parameterized Inapproximability Hypothesis (PIH), which is an analog of the PCP theorem in parameterized complexity, asserts that, there is a constant $\varepsilon> 0$ such that for any computable function $f:\mathbb{N}\to\mathbb{N}$,…
While model checking PCTL for Markov chains is decidable in polynomial-time, the decidability of PCTL satisfiability, as well as its finite model property, are long standing open problems. While general satisfiability is an intriguing…
The concept of self-testing (or rigidity) refers to the fact that for certain Bell inequalities the maximal violation can be achieved in an essentially unique manner. In this work we present a family of Bell inequalities which are maximally…