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In this paper we provide an overview of a series of recent results regarding algorithms for searching for subsequences in words or for the analysis of the sets of subsequences occurring in a word.
Generalizations of linear numeration systems in which the set of natural numbers is recognizable by finite automata are obtained by describing an arbitrary infinite regular language following the lexicographic ordering. For these systems of…
This paper introduces new methods based on exponential families for modeling the correlations between words in text and speech. While previous work assumed the effects of word co-occurrence statistics to be constant over a window of several…
The paper is devoted to constructing a random exponential attractor for some classes of stochastic PDE's. We first prove the existence of an exponential attractor for abstract random dynamical systems and study its dependence on a parameter…
We show that bounded families of global classical relativistic strings that can be written as graphs are relatively compact in C0 topology, but their accumulation points include many non relativistic strings. We also provide an alternative…
We introduce the concept of associativity for string functions, where a string function is a unary operation on the set of strings over a given alphabet. We discuss this new property and describe certain classes of associative string…
We speculate on the distribution of primes in exponentially growing, linear recurrence sequences $(u_n)_{n\geq 0}$ in the integers. By tweaking a heuristic which is successfully used to predict the number of prime values of polynomials, we…
Research into the automatic acquisition of lexical information from corpora is starting to produce large-scale computational lexicons containing data on the relative frequencies of subcategorisation alternatives for individual verbal…
First introduced in the study of the Sturmian words, the iterated palindromic closure was recently generalized to pseudopalindromes. This operator allows one to construct words with an infinity of pseudopalindromic prefixes, called…
Recently, a plethora of works have proposed inference-time algorithms (e.g. best-of-n), which incorporate verifiers to assist the generation process. Their quality-efficiency trade-offs have been empirically benchmarked on a variety of…
It is known that binary words containing no $k$ consecutive 1s are enumerated by $k$-step Fibonacci numbers. In this note we discuss the expected value of a random bit in a random word of length $n$ having this property.
Tries are popular data structures for storing a set of strings, where common prefixes are represented by common root-to-node paths. Over fifty years of usage have produced many variants and implementations to overcome some of their…
Free words are elements of a free monoid, generated over an alphabet via the binary operation of concatenation. Casually speaking, a free word is a finite string of letters. Henceforth, we simply refer to them as words. Motivated by recent…
For many standard models of random structure, first-order logic sentences exhibit a convergence phenomenon on random inputs. The most well-known example is for random graphs with constant edge probability, where the probabilities of…
The family of graphs of reduced words of a certain subcollection of permutations in the union $\cup_{n\geq 4}\frak{S}_{n}$ of symmetic groups is investigated. The subcollection is characterised by the hook cycle type $(n-2,1,1)$ with…
We study various properties of closed relativistic strings. In particular, we characterize their closure under uniform convergence, extending a previous result by Y. Brenier on graph-like unbounded strings, and we discuss some related…
In this work we explore the ability of the Google search engine to find results for random N-letter strings. These random strings, dense over the set of possible N-letter words, address the existence of typos, acronyms, and other words…
Grammar-based compression is a popular and powerful approach to compressing repetitive texts but until recently its relatively poor time-space trade-offs during real-life construction made it impractical for truly massive datasets such as…
Computing the {\em matching statistics} of a string $P[1..m]$ with respect to a text $T[1..n]$ is a fundamental problem which has application to genome sequence comparison. In this paper, we study the problem of computing the matching…
We introduce a string-interval abstract domain, where string intervals are characterized by systems of word equations (encoding lower bounds on string values) and word disequalities (encoding upper bounds). Building upon the lattice…