Abstract
In this chapter we consider for any semigroup S two important families of parts of S. The first is the family Rec(S) of the recognizable subsets of S. A set X ⊆ S is recognizable if it is union of classes of a congruence in S of finite index. The second is the family Rat(S) of the rational subsets of S defined as the smallest family of parts of S containing the finite parts and closed under the rational operations.
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© 1999 Springer-Verlag Berlin Heidelberg
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de Luca, A., Varricchio, S. (1999). Finitely Recognizable Semigroups. In: Finiteness and Regularity in Semigroups and Formal Languages. Monographs in Theoretical Computer Science An EATCS Series. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-59849-4_4
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DOI: https://doi.org/10.1007/978-3-642-59849-4_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-63771-4
Online ISBN: 978-3-642-59849-4
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