Geodesic
Multi-dimensional sets recognizable in all abstract numeration systems
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 46 (2012) no. 1, pp. 51-65

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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.

DOI : 10.1051/ita/2011112
Classification : 68Q45
Keywords: finite automata, numeration systems, recognizable sets of integers, multi-dimensional setting 
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     author = {Charlier, \'Emilie and Lacroix, Anne and Rampersad, Narad},
     title = {Multi-dimensional sets recognizable in all abstract numeration systems},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     pages = {51--65},
     publisher = {EDP-Sciences},
     volume = {46},
     number = {1},
     year = {2012},
     doi = {10.1051/ita/2011112},
     mrnumber = {2904960},
     zbl = {1254.68132},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/ita/2011112/}
}
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Charlier, Émilie; Lacroix, Anne; Rampersad, Narad. Multi-dimensional sets recognizable in all abstract numeration systems. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 46 (2012) no. 1, pp. 51-65. doi: 10.1051/ita/2011112

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