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This paper deals with rational base number systems for p-adic numbers. We mainly focus on the system proposed by Akiyama et al. in 2008, but we also show that this system is in some sense isomorphic to some other rational base number systems by means of finite transducers. We identify the numbers with finite and eventually periodic representations and we… (More)

Let U be a strictly increasing sequence of integers. By a greedy algorithm, every nonnegative integer has a greedy U-representation. The successor function maps the greedy U-representation of N onto the greedy U-representation of N +1. We characterize the sequences U such that the successor function associated to U is a left, resp. a right sequential… (More)

We study expansions in non-integer negative base −β introduced by Ito and Sadahiro [7]. Using countable automata associated with (−β)-expansions, we characterize the case where the (−β)-shift is a system of finite type. We prove that, if β is a Pisot number, then the (−β)-shift is a sofic system. In that case, addition (and more generally normalization on… (More)

Every positive integer can be written as a sum of Fibonacci numbers; it can also be written as a ((nite) sum of (positive and negative) powers of the golden mean '. We show that there exists a letter-to-letter nite two-tape automaton that maps the Fibonacci representation of any positive integer onto its '-expansion, provided the latter is folded around the… (More)

Let be a real number > 1. The digit set conversion between real numbers represented in xed base is shown to be computable by an on-line algorithm, and thus is a continuous function. When is a Pisot number the digit set conversion is computable by an on-line nite automaton.