On the Expressiveness of Real and Integer Arithmetic Automata (Extended Abstract)

If read digit by digit, a n-dimensional vector of integers represented in base r can be viewed as a word over the alphabet r n . It has been known for some time that, under this encoding, the sets of integer vectors recognizable by finite automata are exactly those definable in Presburger arithmetic if independence with respect to the base is required, and those definable in a slight extension of Presburger arithmetic if only a specific base is considered.

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