Strongly locally testable semigroups with commuting idempotents and related languages

نویسنده

  • Carla Selmi
چکیده

If we consider words over the alphabet which is the set of all elements of a semigroup S, then such a word determines an element of S: the product of the letters of the word. S is strongly locally testable if whenever two words over the alphabet S have the same factors of a fixed length k, then the products of the letters of these words are equal. We had previously proved [19] that the syntactic semigroup of a rational language L is strongly locally testable if and only if L is both locally and piecewise testable. We characterize in this paper the variety of strongly locally testable semigroups with commuting idempotents and, using the theory of implicit operations on a variety of semigroups, we derive an elementary combinatorial description of the related variety of languages.

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عنوان ژورنال:
  • ITA

دوره 33  شماره 

صفحات  -

تاریخ انتشار 1999