Émilie Charlier, Anne Lacroix, Narad Rampersad (2012)
RAIRO - Theoretical Informatics and Applications
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We prove that the subsets of that are -recognizable for all abstract numeration systems are exactly the 1-recognizable sets. This generalizes a result of Lecomte and Rigo in the one-dimensional setting.
Paola Bonizzoni, Clelia De Felice, Giancarlo Mauri, Rosalba Zizza (2010)
RAIRO - Theoretical Informatics and Applications
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has been very recently introduced to model a specific recombinant behaviour of circular DNA, continuing the investigation initiated with linear splicing. In this paper we restrict our study to the relationship between and languages generated by and provide some results towards a characterization of the intersection between these two classes. We consider the class of languages , called here , which are closed under conjugacy relation and with being a regular language. Using automata...
Joël Allred, Ulrich Ultes-Nitsche (2012)
RAIRO - Theoretical Informatics and Applications
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In this paper, we define -counting automata as recognizers for -languages, languages of infinite words. We prove that the class of -languages they recognize is a proper extension of the -regular languages. In addition we prove that languages recognized by -counting automata are closed under Boolean operations. It remains an open problem whether or not emptiness is decidable for -counting automata. However, we conjecture strongly...
Mika Hirvensalo, Sebastian Seibert (2010)
RAIRO - Theoretical Informatics and Applications
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We show that the size of a automaton and the size of a complete, minimal automaton accepting a regular language are polynomially related. More precisely, we show that if a regular language is accepted by a Las Vegas automaton having states such that the probability for a definite answer to occur is at least , then , where is the number of the states of the minimal deterministic automaton accepting . Earlier this result has been obtained in [2] by using a reduction to , but here...
Olivier Carton, Ramón Maceiras (2010)
RAIRO - Theoretical Informatics and Applications
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The Rabin index of a rational language of infinite words given by a parity automaton with states is computable in time ( ) where is the cardinality of the alphabet. The number of values used by a parity acceptance condition is always greater than the Rabin index and conversely, the acceptance condition of a parity automaton can always be replaced by an equivalent acceptance condition whose number of used values is exactly the Rabin index. This...