Displaying similar documents to “Rational base number systems for p-adic numbers”

Rational base number systems for p-adic numbers

Christiane Frougny, Karel Klouda (2012)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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This paper deals with rational base number systems for -adic numbers. We mainly focus on the system proposed by Akiyama in 2008, but we also show that this system is in some sense isomorphic to some other rational base number systems by means of finite transducers. We identify the numbers with finite and eventually periodic representations and we also determine the number of representations of a given -adic number.

On the joint 2-adic complexity of binary multisequences

Lu Zhao, Qiao-Yan Wen (2012)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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Joint 2-adic complexity is a new important index of the cryptographic security for multisequences. In this paper, we extend the usual Fourier transform to the case of multisequences and derive an upper bound for the joint 2-adic complexity. Furthermore, for the multisequences with -period, we discuss the relation between sequences and their Fourier coefficients. Based on the relation, we determine a lower bound for the number of multisequences with given joint 2-adic...

The cyclicity problem for the images of Q-rational series

Juha Honkala (2012)

RAIRO - Theoretical Informatics and Applications

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We show that it is decidable whether or not a given Q-rational series in several noncommutative variables has a cyclic image. By definition, a series has a cyclic image if there is a rational number such that all nonzero coefficients of are integer powers of .

The cyclicity problem for the images of Q-rational series

Juha Honkala (2011)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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We show that it is decidable whether or not a given Q-rational series in several noncommutative variables has a cyclic image. By definition, a series has a cyclic image if there is a rational number such that all nonzero coefficients of are integer powers of .

On the joint 2-adic complexity of binary multisequences

Lu Zhao, Qiao-Yan Wen (2012)

RAIRO - Theoretical Informatics and Applications

Similarity:

Joint 2-adic complexity is a new important index of the cryptographic security for multisequences. In this paper, we extend the usual Fourier transform to the case of multisequences and derive an upper bound for the joint 2-adic complexity. Furthermore, for the multisequences with -period, we discuss the relation between sequences and their Fourier coefficients. Based on the relation, we determine a lower bound for the...

One-Rule Length-Preserving Rewrite Systems and Rational Transductions

Michel Latteux, Yves Roos (2014)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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We address the problem to know whether the relation induced by a one-rule length-preserving rewrite system is rational. We partially answer to a conjecture of Éric Lilin who conjectured in 1991 that a one-rule length-preserving rewrite system is a rational transduction if and only if the left-hand side and the right-hand side of the rule of the system are not quasi-conjugate or are equal, that means if and are distinct, there do not exist words , and such that  =  and  = . We prove...

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.

Integers with a maximal number of Fibonacci representations

Petra Kocábová, Zuzana Masáková, Edita Pelantová (2010)

RAIRO - Theoretical Informatics and Applications

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We study the properties of the function which determines the number of representations of an integer as a sum of distinct Fibonacci numbers . We determine the maximum and mean values of for .

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

Similarity:

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.

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

Similarity:

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.

On the structure of (−)-integers

Wolfgang Steiner (2012)

RAIRO - Theoretical Informatics and Applications

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The (−)-integers are natural generalisations of the -integers, and thus of the integers, for negative real bases. When is the analogue of a Parry number, we describe the structure of the set of (−)-integers by a fixed point of an anti-morphism.