Title: Theory / Unimportant / CS / Fundamental / Automata / Number / Integral / 1D / Ultimate periodicity of b-recognisable sets : a quasilinear procedure

Name: A \(b\)-recognisable set
Definition: A set represented by a recognisable/rational/regular language over \(A_b^*\)
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Variables: \(b\ge2\)

Definition: \(\{0,\dots,b-1\}\)
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Variables: \(b\ge2\)
Notation: \(A_b\)

Name: A recognisable set of number
Definition: recognisable subset of \((\mathbb N,+)\)
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Context: Number theory
Definition2: it is the set of lengths of words of a recognisable/rational/regular language over the unary alphabet.
Conjdef: A set \(N\subseteq\mathbb N\) such that, equivalently
Definition3: there exists \(k,l\) such that \(n\in N\iff n+l\in N\) for \(n\ge k\)
Name2: An ultimately periodic set of numbers
Abbreviation2: UP