Related papers: Unique Reconstruction of Coded Strings from Multis…
The number of zeros and the number of ones in a binary string are referred to as the composition of the string, and the prefix-suffix compositions of a string are a multiset formed by the compositions of the prefixes and suffixes of all…
We study the problem of learning a node-labeled tree given independent traces from an appropriately defined deletion channel. This problem, tree trace reconstruction, generalizes string trace reconstruction, which corresponds to the tree…
In the trace reconstruction problem, one seeks to reconstruct a binary string $s$ from a collection of traces, each of which is obtained by passing $s$ through a deletion channel. It is known that $\exp(\tilde O(n^{1/5}))$ traces suffice to…
Consider two or more strings $\mathbf{x}^1,\mathbf{x}^2,\ldots,$ that are concatenated to form $\mathbf{x}=\langle \mathbf{x}^1,\mathbf{x}^2,\ldots \rangle$. Suppose that up to $\delta$ deletions occur in each of the concatenated strings.…
This paper investigates the number of quantum queries made to solve the problem of reconstructing an unknown string from its substrings in a certain query model. More concretely, the goal of the problem is to identify an unknown string $S$…
DNA storage has emerged as an important area of research. The reliability of DNA storage system depends on designing the DNA strings (called DNA codes) that are sufficiently dissimilar. In this work, we introduce DNA codes that satisfy a…
Motivated by DNA storage in living organisms, and by known biological mutation processes, we study the reverse-complement string-duplication system. We fully classify the conditions under which the system has full expressiveness, for all…
Motivated by DNA-based storage applications, we study the problem of reconstructing a coded sequence from multiple traces. We consider the model where the traces are outputs of independent deletion channels, where each channel deletes each…
As the global need for large-scale data storage is rising exponentially, existing storage technologies are approaching their theoretical and functional limits in terms of density and energy consumption, making DNA based storage a potential…
In this paper we study a variant of string pattern matching which deals with tuples of strings known as \textit{multi-track strings}. Multi-track strings are a generalisation of strings (or \textit{single-track strings}) that have primarily…
Determining whether an unordered collection of overlapping substrings (called shingles) can be uniquely decoded into a consistent string is a problem that lies within the foundation of a broad assortment of disciplines ranging from…
In the usual trace reconstruction problem, the goal is to exactly reconstruct an unknown string of length $n$ after it passes through a deletion channel many times independently, producing a set of traces (i.e., random subsequences of the…
We propose a list-decoding scheme for reconstruction codes in the context of uniform-tandem-duplication noise, which can be viewed as an application of the associative memory model to this setting. We find the uncertainty associated with…
DNA as a data storage medium has several advantages, including far greater data density compared to electronic media. We propose that schemes for data storage in the DNA of living organisms may benefit from studying the reconstruction…
The well-known trace reconstruction problem is the problem of inferring an unknown source string $x \in \{0,1\}^n$ from independent "traces", i.e. copies of $x$ that have been corrupted by a $\delta$-deletion channel which independently…
Trace reconstruction is the problem of learning an unknown string $x$ from independent traces of $x$, where traces are generated by independently deleting each bit of $x$ with some deletion probability $q$. In this paper, we initiate the…
A rewriting system is a set of equations over a given set of terms called rules that characterize a system of computation and is a powerful general method for providing decision procedures of equational theories, based upon the principle of…
In this paper we show how string rewriting methods can be applied to give a new method of computing double cosets. Previous methods for double cosets were enumerative and thus restricted to finite examples. Our rewriting methods do not…
It is known that the majority of the human genome consists of repeated sequences. Furthermore, it is believed that a significant part of the rest of the genome also originated from repeated sequences and has mutated to its current form. In…
Repeat finding in strings has important applications in subfields such as computational biology. Surprisingly, all prior work on repeat finding did not consider the constraint on the locality of repeats. In this paper, we propose and study…