Displaying similar documents to “Atoms and partial orders of infinite languages”

On conjugacy of languages

Julien Cassaigne, Juhani Karhumäki, Ján Maňuch (2001)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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

Minimal NFA and biRFSA languages

Michel Latteux, Yves Roos, Alain Terlutte (2009)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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In this paper, we define the notion of biRFSA which is a residual finate state automaton (RFSA) whose the reverse is also an RFSA. The languages recognized by such automata are called biRFSA languages. We prove that the canonical RFSA of a biRFSA language is a minimal NFA for this language and that each minimal NFA for this language is a sub-automaton of the canonical RFSA. This leads to a characterization of the family of biRFSA languages. In the second part of this paper, we define...

Regular languages definable by Lindström quantifiers

Zoltán Ésik, Kim G. Larsen (2003)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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In our main result, we establish a formal connection between Lindström quantifiers with respect to regular languages and the double semidirect product of finite monoids with a distinguished set of generators. We use this correspondence to characterize the expressive power of Lindström quantifiers associated with a class of regular languages.

On the growth rates of complexity of threshold languages

Arseny M. Shur, Irina A. Gorbunova (2010)

RAIRO - Theoretical Informatics and Applications

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Threshold languages, which are the (/(–1))-free languages over -letter alphabets with ≥ 5, are the minimal infinite power-free languages according to Dejean's conjecture, which is now proved for all alphabets. We study the growth properties of these languages. On the base of obtained structural properties and computer-assisted studies we conjecture that the growth rate of complexity of the threshold language over letters tends to a constant α ^ ≈ 1 . 242 as tends to infinity.

Comparing Complexity Functions of a Language and Its Extendable Part

Arseny M. Shur (2008)

RAIRO - Theoretical Informatics and Applications

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Right (left, two-sided) extendable part of a language consists of all words having infinitely many right (resp. left, two-sided) extensions within the language. We prove that for an arbitrary factorial language each of these parts has the same growth rate of complexity as the language itself. On the other hand, we exhibit a factorial language which grows superpolynomially, while its two-sided extendable part grows only linearly.

Formal Languages - Concatenation and Closure

Michał Trybulec (2007)

Formalized Mathematics

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Formal languages are introduced as subsets of the set of all 0-based finite sequences over a given set (the alphabet). Concatenation, the n-th power and closure are defined and their properties are shown. Finally, it is shown that the closure of the alphabet (understood here as the language of words of length 1) equals to the set of all words over that alphabet, and that the alphabet is the minimal set with this property. Notation and terminology were taken from [5] and [13]. MML identifier:...