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Motivated by applications in storage systems and property testing, we study data stream algorithms for local testing and tolerant testing of codes. Ideally, we would like to know whether there exist asymptotically good codes that can be…
Given oracle access to an unknown unitary C from the Clifford group and its conjugate, we give an exact algorithm for identifying C with O(n) queries, which we prove is optimal. We then extend this to all levels of the Gottesman-Chuang…
It is always interesting and important to construct non-Reed-Solomon type MDS codes in coding theory and finite geometries. In this paper, we prove that there are non-Reed-Solomon type MDS codes from arbitrary genus algebraic curves. It is…
A model of computation that is widely used in the formal analysis of reactive systems is symbolic algorithms. In this model the access to the input graph is restricted to consist of symbolic operations, which are expensive in comparison to…
The field of quantum computation currently lacks a formal proof of experimental feasibility. Qubits are fragile and sophisticated quantum error correction is required to achieve reliable quantum computation. The surface code is a promising…
Integer programming (IP) is an important and challenging problem. Approximate methods have shown promising performance on both effectiveness and efficiency for solving the IP problem. However, we observed that a large fraction of variables…
In their seminal 1989 work (IEEE Trans. Inf. Theory 35(3):655-657), Roth and Lempel constructed a well-known family of non-Reed-Solomon maximum distance separable (MDS) codes. For decades, this family of codes has attracted extensive…
An approximate distance oracle is a succinct data structure that provides fast answers to distance queries between any two nodes. In this paper we consider approximate distance oracles for general undirected graphs with non-negative edge…
We continue the study of doubly-efficient proof systems for verifying agnostic PAC learning, for which we obtain the following results. - We construct an interactive protocol for learning the $t$ largest Fourier characters of a given…
This paper presents a novel method of approximating the scalar Wiener-Hopf equation; and therefore constructing an approximate solution. The advantages of this method over the existing methods are reliability and explicit error bounds.…
Implicit time integration is key to robustly simulating stiff materials and large deformations, but its performance is often dominated by repeatedly solving large linear systems. Adaptive coarsening can reduce this cost by concentrating…
Computer Algebra systems are widely spread because of some of their remarkable features such as their ease of use and performance. Nonetheless, this focus on performance sometimes leads to unwanted consequences: algorithms and computations…
In this work, we propose a new bounded arithmetic theory, denoted $APX_1$, designed to formalize a broad class of probabilistic arguments commonly used in theoretical computer science. Under plausible assumptions, $APX_1$ is strictly weaker…
Aggregating data is fundamental to data analytics, data exploration, and OLAP. Approximate query processing (AQP) techniques are often used to accelerate computation of aggregates using samples, for which confidence intervals (CIs) are…
We consider a general model for representing and manipulating parametric curves, in which a curve is specified by a black box mapping a parameter value between 0 and 1 to a point in Euclidean d-space. In this model, we consider the…
Linearity tests are randomized algorithms which have oracle access to the truth table of some function f, and are supposed to distinguish between linear functions and functions which are far from linear. Linearity tests were first…
Light detection and ranging (LiDAR)-based odometry has been widely utilized for pose estimation due to its use of high-accuracy range measurements and immunity to ambient light conditions. However, the performance of LiDAR odometry varies…
Let $\mathcal{H}$ be the Hermitian curve defined over a finite field $\mathbb{F}_{q^2}$. In this paper we complete the geometrical characterization of the supports of the minimum-weight codewords of the algebraic-geometry codes over…
We study grammar-constrained decoding (GCD) as a coupling between an autoregressive next-token distribution and a reachability oracle over a pushdown system compiled from a context-free grammar (CFG). We prove an oracle invariance theorem:…
The statement that one can approximate a quantum torus by some twisted convolution C*-algebra of a (finite) quotient of Z^d can be found in the physics literature dealing with quantum field theory and M-theory. In this paper, we show that…