Displaying similar documents to “A test-set for k-power-free binary morphisms”

Equations on partial words

Francine Blanchet-Sadri, D. Dakota Blair, Rebeca V. Lewis (2007)

RAIRO - Theoretical Informatics and Applications

Similarity:

It is well-known that some of the most basic properties of words, like the commutativity () and the conjugacy (), can be expressed as solutions of word equations. An important problem is to decide whether or not a given equation on words has a solution. For instance, the equation has only periodic solutions in a free monoid, that is, if holds with integers , then there exists a word such that are powers of . This result, which received a lot of attention, was first proved by Lyndon...

Algebraic and graph-theoretic properties of infinite -posets

Zoltán Ésik, Zoltán L. Németh (2010)

RAIRO - Theoretical Informatics and Applications

Similarity:

A -labeled -poset is an (at most) countable set, labeled in the set , equipped with partial orders. The collection of all -labeled -posets is naturally equipped with binary product operations and -ary product operations. Moreover, the -ary product operations give rise to -power operations. We show that those -labeled -posets that can be generated from the singletons by the binary and -ary product operations form the free algebra on in a variety axiomatizable...

Linear size test sets for certain commutative languages

Štěpán Holub, Juha Kortelainen (2010)

RAIRO - Theoretical Informatics and Applications

Similarity:

We prove that for each positive integer the finite commutative language = ( ...) possesses a test set of size at most Moreover, it is shown that each test set for has at least -1 elements. The result is then generalized to commutative languages containing a word such that (i) alph() = alph}(); and (ii) each symbol ∈ alph}() occurs at least twice in if it occurs at least twice in some word of : each such possesses...

On the distribution of characteristic parameters of words

Arturo Carpi, Aldo de Luca (2010)

RAIRO - Theoretical Informatics and Applications

Similarity:

For any finite word on a finite alphabet, we consider the basic parameters and of defined as follows: is the minimal natural number for which has no right special factor of length and is the minimal natural number for which has no repeated suffix of length . In this paper we study the distributions of these parameters, here called characteristic parameters, among the words ...

Complexity of infinite words associated with beta-expansions

Christiane Frougny, Zuzana Masáková, Edita Pelantová (2010)

RAIRO - Theoretical Informatics and Applications

Similarity:

We study the complexity of the infinite word associated with the Rényi expansion of in an irrational base . When is the golden ratio, this is the well known Fibonacci word, which is Sturmian, and of complexity . For such that is finite we provide a simple description of the structure of special factors of the word . When =1 we show that . In the cases when or max} we show that the first difference of the complexity function takes value in for every , and consequently we determine...

Finite repetition threshold for large alphabets

Golnaz Badkobeh, Maxime Crochemore, Michaël Rao (2014)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

Similarity:

We investigate the finite repetition threshold for -letter alphabets, ≥ 4, that is the smallest number for which there exists an infinite -free word containing a finite number of -powers. We show that there exists an infinite Dejean word on a 4-letter alphabet (a word without factors of exponent more than 7/5 ) containing only two 7/5 -powers. For a 5-letter alphabet, we show that there exists an infinite Dejean word containing only 60 5/4 -powers, and we conjecture...