Ostrowski Numeration Systems, Addition and Finite Automata
نویسنده
چکیده
We present an elementary three pass algorithm for computing addition in Ostrowski numerations systems. When a is quadratic, addition in the Ostrowski numeration system based on a is recognizable by a finite automaton. We deduce that a subset of X ⊆Nn is definable in (N,+,Va), where Va is the function that maps a natural number x to the smallest denominator of a convergent of a that appears in the Ostrowski representation based on a of x with a non-zero coefficient, if and only if the set of Ostrowski representations of elements of X is recognizable by a finite automaton. The decidability of the theory of (N,+,Va) follows.
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