Displaying similar documents to “An aperiodicity problem for multiwords”

An aperiodicity problem for multiwords

Véronique Bruyère, Olivier Carton, Alexandre Decan, Olivier Gauwin, Jef Wijsen (2012)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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Multiwords are words in which a single symbol can be replaced by a nonempty set of symbols. They extend the notion of partial words. A word is in a multiword if it occurs in word that can be obtained by selecting one single symbol among the symbols provided in each position of . Motivated by a problem on incomplete databases, we investigate a variant of the pattern matching problem which is to decide whether a word is certain in a multiword . We study the language CERTAIN() of multiwords...

Finite repetition threshold for large alphabets

Golnaz Badkobeh, Maxime Crochemore, Michaël Rao (2014)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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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...

Complexity of infinite words associated with beta-expansions

Christiane Frougny, Zuzana Masáková, Edita Pelantová (2010)

RAIRO - Theoretical Informatics and Applications

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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...

On the distribution of characteristic parameters of words

Arturo Carpi, Aldo de Luca (2010)

RAIRO - Theoretical Informatics and Applications

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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 ...

Linear size test sets for certain commutative languages

Štěpán Holub, Juha Kortelainen (2010)

RAIRO - Theoretical Informatics and Applications

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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...

Forbidden Factors and Fragment Assembly

F. Mignosi, A. Restivo, M. Sciortino (2010)

RAIRO - Theoretical Informatics and Applications

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In this paper methods and results related to the notion of minimal forbidden words are applied to the fragment assembly problem. The fragment assembly problem can be formulated, in its simplest form, as follows: reconstruct a word from a given set of substrings () of a word . We introduce an hypothesis involving the set of fragments and the maximal length of the minimal forbidden factors of . Such hypothesis allows us to reconstruct uniquely the word from the set in linear time....

Equality sets for recursively enumerable languages

Vesa Halava, Tero Harju, Hendrik Jan Hoogeboom, Michel Latteux (2010)

RAIRO - Theoretical Informatics and Applications

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We consider shifted equality sets of the form , where and are nonerasing morphisms and is a letter. We are interested in the family consisting of the languages , where is a coding and is a shifted equality set. We prove several closure properties for this family. Moreover, we show that every recursively enumerable language is a projection of a shifted equality set, that is, for some (nonerasing) morphisms and and...

Undecidability of infinite post correspondence problem for instances of size 8

Jing Dong, Qinghui Liu (2012)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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The infinite Post Correspondence Problem (PCP) was shown to be undecidable by Ruohonen (1985) in general. Blondel and Canterini [36 (2003) 231–245] showed that PCP is undecidable for domain alphabets of size 105, Halava and Harju [40 (2006) 551–557] showed that PCP is undecidable for domain alphabets of size 9. By designing a special coding, we delete a letter from Halava and Harju’s construction. So we prove that PCP is undecidable for domain alphabets of size 8.

Closure properties of hyper-minimized automata

Andrzej Szepietowski (2011)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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Two deterministic finite automata are almost equivalent if they disagree in acceptance only for finitely many inputs. An automaton is hyper-minimized if no automaton with fewer states is almost equivalent to . A regular language is canonical if the minimal automaton accepting is hyper-minimized. The asymptotic state complexity () of a regular language is the number of states of a hyper-minimized automaton for a language finitely different from . In this paper we show...