Sciweavers

CORR
2010
Springer

On the Sets of Real Numbers Recognized by Finite Automata in Multiple Bases

14 years 13 hour ago
On the Sets of Real Numbers Recognized by Finite Automata in Multiple Bases
This article studies the expressive power of finite automata recognizing sets of real numbers encoded in positional notation. We consider Muller automata as well as the restricted class of weak deterministic automata, used as symbolic set representations in actual applications. In previous work, it has been established that the sets of numbers that are recognizable by weak deterministic automata in two bases that do not share the same set of prime factors are exactly those that are definable in the first order additive theory of real and integer numbers. This result extends Cobham's theorem, which characterizes the sets of integer numbers that are recognizable by finite automata in multiple bases. In this article, we first generalize this result to multiplicatively independent bases, which brings it closer to the original statement of Cobham's theorem. Then, we study the sets of reals recognizable by Muller automata in two bases. We show with a counterexample that, in this se...
Bernard Boigelot, Julien Brusten, Véronique
Added 09 Dec 2010
Updated 09 Dec 2010
Type Journal
Year 2010
Where CORR
Authors Bernard Boigelot, Julien Brusten, Véronique Bruyère
Comments (0)