Displaying similar documents to “Strongly locally testable semigroups with commuting idempotents and related languages”

On the decidability of semigroup freeness

Julien Cassaigne, Francois Nicolas (2012)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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This paper deals with the decidability of semigroup freeness. More precisely, the freeness problem over a semigroup is defined as: given a finite subset  ⊆ , decide whether each element of has at most one factorization over . 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. In 1991, Klarner, Birget and Satterfield proved the undecidability...

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...

An aperiodicity problem for multiwords

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

RAIRO - Theoretical Informatics and 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...

On Conjugacy of Languages

Julien Cassaigne, Juhani Karhumäki, Ján Maňuch (2010)

RAIRO - Theoretical Informatics and Applications

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We say that two languages and are conjugates if they satisfy the for some language . We study several problems associated with this equation. For example, we characterize all sets which are conjugated a two-element biprefix set , as well as all two-element sets which are conjugates.

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...

Algebraic and graph-theoretic properties of infinite -posets

Zoltán Ésik, Zoltán L. Németh (2010)

RAIRO - Theoretical Informatics and Applications

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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...

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...

Closure properties of hyper-minimized automata

Andrzej Szepietowski (2012)

RAIRO - Theoretical Informatics and 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...

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...

Regularity of languages defined by formal series with isolated cut point

Alberto Bertoni, Maria Paola Bianchi, Flavi D’Alessandro (2012)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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Let  = { ∈  | ()  } be the language recognized by a formal series :  → ℝ with isolated cut point . We provide new conditions that guarantee the regularity of the language in the case that is rational or is a Hadamard quotient of rational series. Moreover the decidability property of such conditions is investigated.

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...