Languages recognized by finite aperiodic groupoids
We study the context-free languages recognized by a groupoid G in terms of the algebraic properties of the multiplication monoid M(G) of G. Concentrating on the case where M(G) is group-free, we show that all regular languages can be recognized by groupoids for which M(G) is J-trivial and that all groupoids for which M(G) belongs to the larger variety DA recognize only regular languages. Further, we give an example of a groupoid such that M(G) is in the smallest variety outside of DA, and which recognizes all context-free languages not containing the empty word.
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