Related papers: Absent Subsequences in Words
In this paper we consider two problems concerning string factorisation. Specifically given a string $w$ and an integer $k$ find a factorisation of $w$ where each factor has length bounded by $k$ and has the minimum (the FmD problem) or the…
These lecture notes provide an introduction to combinatorics on words and its interactions with dynamics, algebra, and arithmetic. The central theme is the notion of low factor complexity for infinite words. We investigate the following…
We examine words w satisfying the following property: if x is a subword of w and |x| is at least k for some fixed k, then the reversal of x is not a subword of w.
Minimal forbidden factors are a useful tool for investigating properties of words and languages. Two factorial languages are distinct if and only if they have different (antifactorial) sets of minimal forbidden factors. There exist…
The minimizers sampling mechanism is a popular mechanism for string sampling introduced independently by Schleimer et al. [SIGMOD 2003] and by Roberts et al. [Bioinf. 2004]. Given two positive integers $w$ and $k$, it selects the…
It is well-known that checking whether a given string $w$ matches a given regular expression $r$ can be done in quadratic time $O(|w|\cdot |r|)$ and that this cannot be improved to a truly subquadratic running time of $O((|w|\cdot…
In this thesis, a detailed study shows that closed itemsets and minimal generators play a key role for concisely representing both frequent itemsets and association rules. These itemsets structure the search space into equivalence classes…
Many problems in bioinformatics are about finding strings that approximately represent a collection of given strings. We look at more general problems where some input strings can be classified as outliers. The Close to Most Strings problem…
Repetitiveness measures quantify how much repetitive structure a string contains and serve as parameters for compressed representations and indexing data structures. We study the measure $\chi$, defined as the size of the smallest…
We consider the longest common subsequence problem in the context of subsequences with gap constraints. In particular, following Day et al. 2022, we consider the setting when the distance (i. e., the gap) between two consecutive symbols of…
Neural keyphrase generation models have recently attracted much interest due to their ability to output absent keyphrases, that is, keyphrases that do not appear in the source text. In this paper, we discuss the usefulness of absent…
In the deletion channel, an important problem is to determine the number of subsequences derived from a string $U$ of length $n$ when subjected to $t$ deletions. It is well-known that the number of subsequences in the setting exhibits a…
Take any word over some alphabet. If it is non-empty, go to any position and print out the letter being scanned. Now repeat the following any number of times (possibly zero): either stay at the current letter, or move one letter leftwards…
For a text given in advance, the substring minimal suffix queries ask to determine the lexicographically minimal non-empty suffix of a substring specified by the location of its occurrence in the text. We develop a data structure answering…
Two words $w_1$ and $w_2$ are said to be $k$-binomial equivalent if every non-empty word $x$ of length at most $k$ over the alphabet of $w_1$ and $w_2$ appears as a scattered factor of $w_1$ exactly as many times as it appears as a…
Let w be a binary string and let a_w (n) be the number of occurrences of the word w in the binary expansion of n. As usual we let s(n) denote the Stern sequence; that is, s(0)=0, s(1)=1, and for n >= 1, s(2n)=s(n) and s(2n+1)=s(n)+s(n+1).…
Latent or unobserved phenomena pose a significant difficulty in data analysis as they induce complicated and confounding dependencies among a collection of observed variables. Factor analysis is a prominent multivariate statistical modeling…
We consider several novel aspects of unique factorization in formal languages. We reprove the familiar fact that the set uf(L) of words having unique factorization into elements of L is regular if L is regular, and from this deduce an…
A weighted string over an alphabet of size $\sigma$ is a string in which a set of letters may occur at each position with respective occurrence probabilities. Weighted strings, also known as position weight matrices or uncertain sequences,…
A {\it superpattern} is a string of characters of length $n$ that contains as a subsequence, and in a sense that depends on the context, all the smaller strings of length $k$ in a certain class. We prove structural and probabilistic results…