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

  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},
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


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