Multi-dimensional sets recognizable in all abstract numeration systems
Received: 2 November 2010
Accepted: 29 June 2011
We prove that the subsets of 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.
Mathematics Subject Classification: 68Q45
Key words: Finite automata / numeration systems / recognizable sets of integers / multi-dimensional setting
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