A Generalization of Semenov's Theorem to Automata over Real Numbers

@inproceedings{Boigelot2009AGO,
title={A Generalization of Semenov's Theorem to Automata over Real Numbers},
author={Bernard Boigelot and Julien Brusten and J{\'e}r{\^o}me Leroux},
booktitle={CADE},
year={2009}
}

This work studies the properties of finite automata recognizing vectors with real components, encoded positionally in a given integer numeration base. Such automata are used, in particular, as symbolic data structures for representing sets definable in the first-order theory 〈R, Z, +,≤〉, i.e., the mixed additive arithmetic of integer and real variables. They also lead to a simple decision procedure for this arithmetic. In previous work, it has been established that the sets definable in 〈R, Z… CONTINUE READING