Multi-dimensional sets recognizable in all abstract numeration systems

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Author

Charlier, Émilie
Lacroix, Anne
Rampersad, Narad

Uri

http://hdl.handle.net/10680/1411

Date

2011

Doi

10.1051/ita/2011112

Citation

Charlier, É., A. Lacroix, and N. Rampersad. “Multi-dimensional sets recognizable in all abstract numeration systems.” Theor. Inform. Appl. 46 (2012), 51-65. DOI: 10.1051/ita/2011112.

Abstract

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.

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