Related papers: On an algorithm for multiperiodic words
Timed words are words where letters of the alphabet come with time stamps. We extend the definitions of semistandard tableaux, insertion, Knuth equivalence, and the plactic monoid to the setting of timed words. Using this, Greene's theorem…
A notion of alternating timed automata is proposed. It is shown that such automata with only one clock have decidable emptiness problem over finite words. This gives a new class of timed languages which is closed under boolean operations…
Let $\widetilde{\alpha}$ be a length-$L$ cyclic sequence of characters from a size-$K$ alphabet $\mathcal{A}$ such that the number of occurrences of any length-$m$ string on $\mathcal{A}$ as a substring of $\widetilde{\alpha}$ is $\lfloor L…
In this paper we explore various interconnections between rich words, Sturmian words, and trapezoidal words. Rich words, first introduced in arXiv:0801.1656 by the second and third authors together with J. Justin and S. Widmer, constitute a…
We survey and unify recent results on the existence of accurate algorithms for evaluating multivariate polynomials, and more generally for accurate numerical linear algebra with structured matrices. By "accurate" we mean that the computed…
We introduce the notion of unavoidable (complete) sets of word patterns, which is a refinement for that of words, and study certain numerical characteristics for unavoidable sets of patterns. In some cases we employ the graph of pattern…
Given a text $T$ of length $n$ and a pattern $P$ of length $m$, the string matching problem is a task to find all occurrences of $P$ in $T$. In this study, we propose an algorithm that solves this problem in $O((n + m)q)$ time considering…
In dictionary selection, several atoms are selected from finite candidates that successfully approximate given data points in the sparse representation. We propose a novel efficient greedy algorithm for dictionary selection. Not only does…
In this paper, we describe an approach to sentence categorization which has the originality to be based on natural properties of languages with no training set dependency. The implementation is fast, small, robust and textual errors…
This article presents a combinatorial result on indexed languages which was inspired by an attempt to understand the structure of groups with indexed language word problem. We show that a sufficiently long word in an indexed language can be…
In this paper, we explore applications of combinatorics on words across various domains, including data compression, error detection, cryptographic protocols, and pseudorandom number generation. The examination of the theoretical…
In this work we were aimed to study music using visibility algorithms. This algorithms are used as a way to get a network, from a time series. However the main idea of this paper was not to study music from the perspective of complex…
In this paper we describe an algorithm for aligning sentences with their translations in a bilingual corpus using lexical information of the languages. Existing efficient algorithms ignore word identities and consider only the sentence…
We determine the maximal length of the period of a periodic word defined by $n$ restrictions. It happens to be the corresponding Fibonacci number.
We construct multiperiodic processes -- a simple example of stationary ergodic (but not mixing) processes over natural numbers that enjoy the vanishing entropy rate under a mild condition. Multiperiodic processes are supported on randomly…
Constantinescu and Ilie (Bulletin of the EATCS 89, 167-170, 2006) introduced the idea of an Abelian period with head and tail of a finite word. An Abelian period is called full if both the head and the tail are empty. We present a simple…
In multiobjective optimization, the result of an optimization algorithm is a set of efficient solutions from which the decision maker selects one. It is common that not all the efficient solutions can be computed in a short time and the…
A run in a string is a maximal periodic substring. For example, the string $\texttt{bananatree}$ contains the runs $\texttt{anana} = (\texttt{an})^{3/2}$ and $\texttt{ee} = \texttt{e}^2$. There are less than $n$ runs in any length-$n$…
A word-representable graph is a simple graph $G$ which can be represented by a word $w$ over the vertices of $G$ such that any two vertices are adjacent in $G$ if and only if they alternate in $w$. It is known that the class of…
We present a polynomial time algorithm that constructs a deterministic parity automaton (DPA) from a given set of positive and negative ultimately periodic example words. We show that this algorithm is complete for the class of…