Related papers: Sequence Reconstruction Problem for Ternary Deleti…

The goal of trace reconstruction is to reconstruct an unknown $n$-bit string $x$ given only independent random traces of $x$, where a random trace of $x$ is obtained by passing $x$ through a deletion channel. A Statistical Query (SQ)…

In the \emph{trace reconstruction problem}, an unknown source string $x \in \{0,1\}^n$ is transmitted through a probabilistic \emph{deletion channel} which independently deletes each bit with some fixed probability $\delta$ and concatenates…

This paper considers a binary channel with deletions and insertions, where each input bit is transformed in one of the following ways: it is deleted with probability d, or an extra bit is added after it with probability i, or it is…

In this paper, we investigate the reconstruction of permutations on {1, 2, ..., n} from betweenness constraints involving the minimum and the maximum element located between t and t+1, for all t=1, 2, ..., n-1. We propose two variants of…

This paper studies the problem of constructing codes correcting deletions in arrays. Under this model, it is assumed that an $n\times n$ array can experience deletions of rows and columns. These deletion errors are referred to as…

We consider the problem of designing low-redundancy codes in settings where one must correct deletions in conjunction with substitutions or adjacent transpositions; a combination of errors that is usually observed in DNA-based data storage.…

Tree trace reconstruction aims to learn the binary node labels of a tree, given independent samples of the tree passed through an appropriately defined deletion channel. In recent work, Davies, R\'acz, and Rashtchian used combinatorial…

The problem of reconstructing strings from their substring spectra has a long history and in its most simple incarnation asks for determining under which conditions the spectrum uniquely determines the string. We study the problem of coded…

\emph{Population recovery} is the problem of learning an unknown distribution over an unknown set of $n$-bit strings, given access to independent draws from the distribution that have been independently corrupted according to some noise…

We investigate the problem of encoding data into an $(n, t)$-break-resilient code ($(n, t)$-BRC), i.e., a collections of sequences of length~$n$ from which the original data can be reconstructed even if they are adversarially broken at up…

In recent years, the emergence of DNA storage systems has led to a widespread focus on the research of codes correcting insertions, deletions, and classic substitutions. During the initial investigation, Levenshtein discovered the VT codes…

This paper studies reconstruction of strings based upon their substrings spectrum. Under this paradigm, it is assumed that all substrings of some fixed length are received and the goal is to reconstruct the string. While many existing works…

In distance query reconstruction, we wish to reconstruct the edge set of a hidden graph by asking as few distance queries as possible to an oracle. Given two vertices $u$ and $v$, the oracle returns the shortest path distance between $u$…

For a given $n$, what is the smallest number $k$ such that every sequence of length $n$ is determined by the multiset of all its $k$-subsequences? This is called the $k$-deck problem for sequence reconstruction, and has been generalized to…

In this paper, we consider a broadcasting process in which information is propagated from a given root node on a noisy tree network, and answer the question that whether the symbols at the nth level of the tree contain non-vanishing…

We consider deletion correcting codes over a q-ary alphabet. It is well known that any code capable of correcting s deletions can also correct any combination of s total insertions and deletions. To obtain asymptotic upper bounds on code…

We study the trace reconstruction problem for spider graphs. Let $n$ be the number of nodes of a spider and $d$ be the length of each leg, and suppose that we are given independent traces of the spider from a deletion channel in which each…

In this paper, we propose a partitioning technique that decomposes a pair of sequences with overlapping $t$-deletion $s$-substitution balls into sub-pairs, where the $^{\leq}t$-burst-deletion balls of each sub-pair intersect. This…

Modern neural sequence generation models are built to either generate tokens step-by-step from scratch or (iteratively) modify a sequence of tokens bounded by a fixed length. In this work, we develop Levenshtein Transformer, a new partially…

Consider the task of locating an unknown target point using approximate distance queries: in each round, a reconstructor selects a query point and receives a noisy version of its distance to the target. This problem arises naturally in…