The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

Displaying 541 – 560 of 893

Showing per page

On some problems related to palindrome closure

Michelangelo Bucci, Aldo de Luca, Alessandro De Luca, Luca Q. Zamboni (2008)

RAIRO - Theoretical Informatics and Applications

In this paper, we solve some open problems related to (pseudo)palindrome closure operators and to the infinite words generated by their iteration, that is, standard episturmian and pseudostandard words. We show that if ϑ is an involutory antimorphism of A*, then the right and left ϑ-palindromic closures of any factor of a ϑ-standard word are also factors of some ϑ-standard word. We also introduce the class of pseudostandard words with “seed”, obtained by iterated pseudopalindrome closure starting...

On some properties of doubly-periodic words

Claudio Baiocchi (1997)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

We study the functional equation: 1 A B C = C D A where A , B , C and D are words over an alphabet A . In particular we prove a «structure result» for the inner factors B , D : for suitably chosen words X , Y , Z one has: 2 B = X Y Z , D = Z Y X 2 ⁢...

On subgraphs without large components

Glenn G. Chappell, John Gimbel (2017)

Mathematica Bohemica

We consider, for a positive integer k , induced subgraphs in which each component has order at most k . Such a subgraph is said to be k -divided. We show that finding large induced subgraphs with this property is NP-complete. We also consider a related graph-coloring problem: how many colors are required in a vertex coloring in which each color class induces a k -divided subgraph. We show that the problem of determining whether some given number of colors suffice is NP-complete, even for 2 -coloring...

On substitution invariant Sturmian words: an application of Rauzy fractals

Valérie Berthé, Hiromi Ei, Shunji Ito, Hui Rao (2007)

RAIRO - Theoretical Informatics and Applications

Sturmian words are infinite words that have exactly n+1 factors of length n for every positive integer n. A Sturmian word sα,p is also defined as a coding over a two-letter alphabet of the orbit of point ρ under the action of the irrational rotation Rα : x → x + α (mod 1). A substitution fixes a Sturmian word if and only if it is invertible. The main object of the present paper is to investigate Rauzy fractals associated with two-letter invertible substitutions. As an application, we give...

On synchronized sequences and their separators

Arturo Carpi, Cristiano Maggi (2001)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

We introduce the notion of a k -synchronized sequence, where k is an integer larger than 1. Roughly speaking, a sequence of natural numbers is said to be k -synchronized if its graph is represented, in base k , by a right synchronized rational relation. This is an intermediate notion between k -automatic and k -regular sequences. Indeed, we show that the class of k -automatic sequences is equal to the class of bounded k -synchronized sequences and that the class of k -synchronized sequences is strictly...

On synchronized sequences and their separators

Arturo Carpi, Cristiano Maggi (2010)

RAIRO - Theoretical Informatics and Applications

We introduce the notion of a k-synchronized sequence, where k is an integer larger than 1. Roughly speaking, a sequence of natural numbers is said to be k-synchronized if its graph is represented, in base k, by a right synchronized rational relation. This is an intermediate notion between k-automatic and k-regular sequences. Indeed, we show that the class of k-automatic sequences is equal to the class of bounded k-synchronized sequences and that the class of k-synchronized sequences is...

On the computational complexity of centers locating in a graph

Ján Plesník (1980)

Aplikace matematiky

It is shown that the problem of finding a minimum k -basis, the n -center problem, and the p -median problem are N P -complete even in the case of such communication networks as planar graphs with maximum degree 3. Moreover, a near optimal m -center problem is also N P -complete.

On the computational complexity of (O,P)-partition problems

Jan Kratochvíl, Ingo Schiermeyer (1997)

Discussiones Mathematicae Graph Theory

We prove that for any additive hereditary property P > O, it is NP-hard to decide if a given graph G allows a vertex partition V(G) = A∪B such that G[A] ∈ 𝓞 (i.e., A is independent) and G[B] ∈ P.

On the conjectures of Rauzy and Shallit for infinite words

Jean-Paul Allouche, Mireille Bousquet-Mélou (1995)

Commentationes Mathematicae Universitatis Carolinae

We show a connection between a recent conjecture of Shallit and an older conjecture of Rauzy for infinite words on a finite alphabet. More precisely we show that a Rauzy-like conjecture is equivalent to Shallit's. In passing we correct a misprint in Rauzy's conjecture.

On the D0L Repetition Threshold

Ilya Goldstein (2010)

RAIRO - Theoretical Informatics and Applications

The repetition threshold is a measure of the extent to which there need to be consecutive (partial) repetitions of finite words within infinite words over alphabets of various sizes. Dejean's Conjecture, which has been recently proven, provides this threshold for all alphabet sizes. Motivated by a question of Krieger, we deal here with the analogous threshold when the infinite word is restricted to be a D0L word. Our main result is that, asymptotically, this threshold does not exceed the unrestricted...

On the decidability of semigroup freeness∗

Julien Cassaigne, Francois Nicolas (2012)

RAIRO - Theoretical Informatics and Applications

This paper deals with the decidability of semigroup freeness. More precisely, the freeness problem over a semigroup S is defined as: given a finite subset X ⊆ S, decide whether each element of S has at most one factorization over X. To date, the decidabilities of the following two freeness problems have been closely examined. In 1953, Sardinas and Patterson proposed a now famous algorithm for the freeness problem over the free monoids....

Currently displaying 541 – 560 of 893