Strongly locally testable semigroups with commuting idempotents and related languages

Carla Selmi

RAIRO - Theoretical Informatics and Applications (2010)

  • Volume: 33, Issue: 1, page 47-57
  • ISSN: 0988-3754

Abstract

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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.

How to cite

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Selmi, Carla. "Strongly locally testable semigroups with commuting idempotents and related languages." RAIRO - Theoretical Informatics and Applications 33.1 (2010): 47-57. <http://eudml.org/doc/222035>.

@article{Selmi2010,
abstract = { 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. },
author = {Selmi, Carla},
journal = {RAIRO - Theoretical Informatics and Applications},
keywords = {strongly locally testable semigroups with commuting idempotents},
language = {eng},
month = {3},
number = {1},
pages = {47-57},
publisher = {EDP Sciences},
title = {Strongly locally testable semigroups with commuting idempotents and related languages},
url = {http://eudml.org/doc/222035},
volume = {33},
year = {2010},
}

TY - JOUR
AU - Selmi, Carla
TI - Strongly locally testable semigroups with commuting idempotents and related languages
JO - RAIRO - Theoretical Informatics and Applications
DA - 2010/3//
PB - EDP Sciences
VL - 33
IS - 1
SP - 47
EP - 57
AB - 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.
LA - eng
KW - strongly locally testable semigroups with commuting idempotents
UR - http://eudml.org/doc/222035
ER -

References

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