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The minimal automaton recognizing mN in a linear numeration system
We study the structure of automata accepting the greedy representations of N in a wide class of numeration systems. We describe the conditions under which such automata can have more than one strongly connected component ...
Multi-dimensional sets recognizable in all abstract numeration systems
(EDP Sciences, 2011)
We prove that the subsets of Nd that are S-recognizable for all abstract numeration systems S are exactly the 1-recognizable sets. This generalizes a result of Lecomte and Rigo in the one-dimensional setting.