Abstract
Let U be a strictly increasing sequence of integers, and let L(U) be the set of greedy U-representations of all the nonnegative integers. The successor function maps the greedy U-representation of N onto the greedy U-representation of N+1. We show that the successor function associated to U is computable by a finite 2-tape automaton if and only if the set L(U) is recognizable by a finite automaton.
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