Related papers: String Attractors and Infinite Words
We propose novel algorithms for sequence prediction based on ideas from stringology. These algorithms are time and space efficient and satisfy mistake bounds related to particular stringological complexity measures of the sequence. In this…
String matching is the problem of deciding whether a given $n$-bit string contains a given $k$-bit pattern. We study the complexity of this problem in three settings. Communication complexity. For small $k$, we provide near-optimal upper…
The combinatorics of reduced words and commutation classes plays an important role in geometric representation theory. A string polytope is a lattice polytope associated to each reduced word of the longest element $w_0$ in the symmetric…
We study how much injective morphisms can increase the repetitiveness of a given word. This question has a few possible variations depending on the meaning of ``repetitiveness''. We concentrate on fractional exponents of finite words and…
How can we compress language models without sacrificing accuracy? The number of compression algorithms for language models is rapidly growing to benefit from remarkable advances of recent language models without side effects due to the…
We systematically investigate the complexity of model checking the existential positive fragment of first-order logic. In particular, for a set of existential positive sentences, we consider model checking where the sentence is restricted…
We study the fundamental problem of finding the best string to represent a given set, in the form of the Closest String problem: Given a set $X \subseteq \Sigma^d$ of $n$ strings, find the string $x^*$ minimizing the radius of the smallest…
The Kolmogorov complexity of x, denoted C(x), is the length of the shortest program that generates x. For such a simple definition, Kolmogorov complexity has a rich and deep theory, as well as applications to a wide variety of topics…
Numbers and numerical vectors account for a large portion of data. However, recently the amount of string data generated has increased dramatically. Consequently, classifying string data is a common problem in many fields. The most widely…
We study a two-parameter family of one-dimensional maps and related (a,b)-continued fractions suggested for consideration by Don Zagier. We prove that the associated natural extension maps have attractors with finite rectangular structure…
The Suffix Array is a classic text index enabling on-line pattern matching queries via simple binary search. The main drawback of the Suffix Array is that it takes linear space in the text's length, even if the text itself is extremely…
In this work, we consider the satisfiability problem in a logic that combines word equations over string variables denoting words of unbounded lengths, regular languages to which words belong and Presburger constraints on the length of…
Searching for all occurrences of a pattern in a text is a fundamental problem in computer science with applications in many other fields, like natural language processing, information retrieval and computational biology. In the last two…
The circular dictionary matching problem is an extension of the classical dictionary matching problem where every string in the dictionary is interpreted as a circular string: after reading the last character of a string, we can move back…
The factor complexity function $C_w(n)$ of a finite or infinite word $w$ counts the number of distinct factors of $w$ of length $n$ for each $n \ge 0$. A finite word $w$ of length $|w|$ is said to be trapezoidal if the graph of its factor…
We study first-order model checking, by which we refer to the problem of deciding whether or not a given first-order sentence is satisfied by a given finite structure. In particular, we aim to understand on which sets of sentences this…
This paper is concerned with the study of the consistency of a variational method for probability measure quantization, deterministically realized by means of a minimizing principle, balancing power repulsion and attraction potentials. The…
We present a new algorithm for subsequence matching in grammar compressed strings. Given a grammar of size $n$ compressing a string of size $N$ and a pattern string of size $m$ over an alphabet of size $\sigma$, our algorithm uses…
A square is the concatenation of a nonempty word with itself. A word has period p if its letters at distance p match. The exponent of a nonempty word is the quotient of its length over its smallest period. In this article we give a proof of…
Amidst all candidates of physics beyond the Standard Model, string theory provides a unique proposal for incorporating gauge and gravitational interactions. In string theory, a four-dimensional theory that unifies quantum mechanics and…