Multi-dimensional sets recognizable in all abstract numeration systems
Emilie Charlier, Anne Lacroix, Narad Rampersad
TL;DR
This paper characterizes multi-dimensional sets that are recognizable across all abstract numeration systems, showing they are exactly the 1-recognizable sets, thus generalizing previous one-dimensional results.
Contribution
It extends the characterization of recognizable sets from one dimension to multiple dimensions in the context of all abstract numeration systems.
Findings
Multi-dimensional S-recognizable sets are exactly the 1-recognizable sets.
Generalizes Lecomte and Rigo's one-dimensional result to higher dimensions.
Provides a complete classification of sets recognizable in all abstract numeration systems.
Abstract
We prove that the subsets of N^d 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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Taxonomy
Topicssemigroups and automata theory · Computability, Logic, AI Algorithms · Advanced Topology and Set Theory