Syntactic Semigroups

@inproceedings{Pin1997SyntacticS,
  title={Syntactic Semigroups},
  author={Jean-{\'E}ric Pin},
  booktitle={Handbook of Formal Languages},
  year={1997}
}
  • J. Pin
  • Published in Handbook of Formal Languages 1 April 1997
  • Economics
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262 Citations
Highly Influential Citations
25
Background Citations
122
Methods Citations
21
Results Citations
4

262 Citations

Syntactic Semiring of a Language
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This thesis provides a generic approach, based on combinatorial arguments, to proving the decidability of the separation problem for several subclasses of the regular languages, including the classes of piecewise testable languages, unambiguous languages, and locally (threshold) testable Languages.
Well quasi-orders arising from finite ordered semigroups
In 1985, Bucher, Ehrenfeucht and Haussler studied derivation relations associated with a given set of context-free rules. Their research motivated a question regarding homomorphisms from the…
Syntactic semigroup problem for the semigroup reducts of Affine Near-semirings over Brandt Semigroups
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This work investigates the syntactic semigroup problem for both the semigroup reducts of A+(B n), the affine near-semiring over a Brandt semigroup Bn.
A Robust Class of Regular Languages
TLDR
This survey paper presents known results and open questions on a proper subclass of the class of regular languages, denoted by $\mathcal{W}$, and proposes as a challenge to find a constructive description and a logical characterization of this class.
Bridges for Concatenation Hierarchies
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This article solves positively a question raised in 1985 about concatenation hierarchies of rational languages, which are constructed by alternating boolean operations and concate-nation products, and establishes a simple algebraic connection between the Straubing-Therien hierarchy and the group hierarchy.
Algebraic classifications of regular tree languages
We review several algebraic formalisms used for characterizing families of regular tree languages. A theory based on syntactic algebras and varieties of congruences is presented in detail, including…
Densification via polynomials, languages, and frames
A positive extension of Eilenberg’s variety theorem for non-regular languages
TLDR
This paper introduces the so-called positively typed monoids, and gives a correspondence between varieties of such algebraic structures and positive varieties of possibly non-regular languages.
Proving that a Tree Language is not First-Order Definable
TLDR
It is shown that a recursive proof exists for the syntactic algebra of every non-definable language and an algebra of mappings and an extended algebra is defined, which is used to redefine the notion of aperiodicity in a way that generalizes the existing ones.
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References

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L’accès aux archives de la revue « Revue française d’automatique informatique recherche opérationnelle • Informatique théorique » implique l’ Accord avec les conditions générales d‘utilisation.
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TLDR
The main goal is to point out the similarities and distinctions between C-varieties and varieties of finite monoids that underlie the more traditional approach to the theory.
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