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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

The syntactic monoid of an infix code


Authors: Mario Petrich and Gabriel Thierrin
Journal: Proc. Amer. Math. Soc. 109 (1990), 865-873
MSC: Primary 68Q45
DOI: https://doi.org/10.1090/S0002-9939-1990-1010804-6
MathSciNet review: 1010804
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Abstract: Necessary and sufficient conditions on a monoid $ M$ are found in order that $ M$ be isomorphic to the syntactic monoid of a language $ L$ over an alphabet $ X$ having one of the following properties. In the first theorem $ L$ is a $ {P_L}$-class and $ {P_{W\left( L \right)}} \subseteq {P_L}$ where $ {P_L}$ is the syntactic congruence of $ L$ and $ W\left( L \right)$ is the residue of $ L$. In the second theorem $ L$ is an infix code; that is, satisfies $ u,uvw \in L$ implying $ u = w = 1$. In the third theorem $ L$ is an infix code satisfying a condition which amounts to the requirement that $ M$ be a nilmonoid. Various refinements of these conditions are also considered.


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DOI: https://doi.org/10.1090/S0002-9939-1990-1010804-6
Keywords: Monoid, language, congruence, syntactic, code, infix
Article copyright: © Copyright 1990 American Mathematical Society