Abstract
This paper studies the expressive power of finite-state automata recognizing sets of real numbers encoded positionally. It is known that the sets that are definable in the first-order additive theory of real and integer variables (ℝ, ℤ, +, 1. In this paper, we prove the reciprocal property, i.e., that a subset of R that is recognizable by weak deterministic automata in every base r > 1 is necessarily definable in (ℝ, ℤ, +,
Cite
CITATION STYLE
Boigelot, B., & Brusten, J. (2007). A generalization of Cobham’s theorem to automata over real numbers. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 4596 LNCS, pp. 813–824). Springer Verlag. https://doi.org/10.1007/978-3-540-73420-8_70
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