The syntactic monoid of an infix code
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- by Mario Petrich and Gabriel Thierrin PDF
- Proc. Amer. Math. Soc. 109 (1990), 865-873 Request permission
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.References
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Additional Information
- © Copyright 1990 American Mathematical Society
- 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