#### Filter Results:

- Full text PDF available (56)

#### Publication Year

1979

2017

- This year (1)
- Last 5 years (9)
- Last 10 years (29)

#### Publication Type

#### Co-author

#### Journals and Conferences

#### Key Phrases

Learn More

- Christiane Frougny, Jacques Sakarovitch
- Theor. Comput. Sci.
- 1993

- Christiane Frougny
- Inf. Comput.
- 1988

- Christiane Frougny
- Mathematical systems theory
- 1992

Numeration systems, the basis of which is defined by a linear recurrence with integer coefficients, are considered. We give conditions on the recurrence under which the function of normalization which transforms any representation of an integer into the normal one—obtained by the usual algorithm—can be realized by a finite automaton. Addition is a… (More)

- Christiane Frougny, Jacques Sakarovitch
- STACS
- 1991

The purpose of this paper is the s tudy of the rational relations tha t is relations on words that are computable by finite 2-tape au tomata with the Proper ty that the difference of the length of two words in relation is bounded. The first motivat ion for this work has been the problem of representations of integers by means of non classical numerat ion… (More)

- Daniel Berend, Christiane Frougny
- Mathematical systems theory
- 1994

We prove that the function of normalization in base θ, which maps any θ-representation of a real number onto its θ-development, obtained by a greedy algorithm, is a function computable by a finite automaton over any alphabet if and only if θ is a Pisot number.

- Christiane Frougny
- LATIN
- 2002

A new method for representing positive integers and real numbers in a rational base is considered. It amounts to computing the digits from right to left, least significant first. Every integer has a unique such expansion. The set of expansions of the integers is not a regular language but nevertheless addition can be performed by a letter-to-letter finite… (More)

- Christiane Frougny
- Inf. Comput.
- 1997

Let U be a strictly increasing sequence of integers. By a greedy algorithm, every nonnegative integer has a greedy U -representation. The successor function maps the greedy U -representation of N onto the greedy U -representation of N+1. We characterize the sequences U such that the successor function associated to U is a left, resp. a right sequential… (More)

- Christiane Frougny, Jacques Sakarovitch
- IJAC
- 1999

Every positive integer can be written as a sum of Fibonacci numbers; it can also be written as a ((nite) sum of (positive and negative) powers of the golden mean '. We show that there exists a letter-to-letter nite two-tape automaton that maps the Fibonacci representation of any positive integer onto its '-expansion, provided the latter is folded around the… (More)

- Christiane Frougny, Anna Chiara Lai
- Developments in Language Theory
- 2009

We study expansions in non-integer negative base −β introduced by Ito and Sadahiro [7]. Using countable automata associated with (−β)-expansions, we characterize the case where the (−β)-shift is a system of finite type. We prove that, if β is a Pisot number, then the (−β)-shift is a sofic system. In that case, addition (and more generally normalization on… (More)