# 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
Syntactic Semiring of a Language
Pin's refinement of Eilenberg theorem gives a one-to-one correspondence between positive varieties of rational languages and pseudovarieties of ordered monoids.
A combinatorial approach to the separation problem for regular languages. (Une approche combinatoire du problème de séparation pour les langages réguliers)
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
• Mathematics
DLT
• 2022
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
• Mathematics
ArXiv
• 2015
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
• Mathematics
MFCS
• 2008
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
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
A positive extension of Eilenberg’s variety theorem for non-regular languages
• Mathematics, Computer Science
Applicable Algebra in Engineering, Communication and Computing
• 2020
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
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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