Computability by finite automata and Pisot bases
Mathematical Systems Theory
Automata, Languages, and Machines
Automata, Languages, and Machines
The definable criterion for definability in Presburger arithmetic and its applications
Theoretical Computer Science
A Polynomial Time Presburger Criterion and Synthesis for Number Decision Diagrams
LICS '05 Proceedings of the 20th Annual IEEE Symposium on Logic in Computer Science
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Numbers do exist, independently of the way we represent them, of the way we write them. And there are many ways to write them: integers as finite sequence of digits once a base is fixed, rational numbers as a pair of integer or as an ultimately periodic infinite sequence of digits, or reals as an infinite sequence of digits but also as a continued fraction, just to quote a few. Operations on numbers are defined, independently of the way they are computed. But when they are computed they amounts to be algorithms that work on the representations of numbers.