Do Long Van Ensembles code-compatibles et une généralisation du théorème de Sardinas-Patterson. (French) Zbl 0574.20053 Theor. Comput. Sci. 38, 123-132 (1985). Author’s abstract: One denotes by \(A^{\infty}\) the monoid of all finite and infinite words over an alphabet \(A\). The code-compatibility of a pair \((X,Y)\) of subsets of \(A^{\infty}\) is here defined. A necessary and sufficient condition, which is a generalization of the Sardinas-Patterson theorem [IER Conv. Record 8, 104–108 (1953)], for \((X,Y)\) to be code-compatible is established. It is shown that the class of the submonoids of \(A^{\infty}\) generated by an infinitary code is closed under intersection, and also that, for any two infinitary codes \(X\) and \(Y\), \(X^*\cap Y^*=(X\cap Y)^*\) iff (X,Y) is code-compatible.” Reviewer: Bedřich Pondělíček (Praha) Cited in 2 Documents MSC: 20M35 Semigroups in automata theory, linguistics, etc. 68Q45 Formal languages and automata Keywords:infinite words; code-compatibility; Sardinas-Patterson theorem; submonoids; infinitary code PDF BibTeX XML Cite \textit{Do Long Van}, Theor. Comput. Sci. 38, 123--132 (1985; Zbl 0574.20053) Full Text: DOI OpenURL References: [1] Berstel, J.; Perrin, D.; Schützenberger, M.P., Théorie des codes, (1981), LITP Paris, Chapitres I-IV [2] Eilenberg, S., () [3] Riley, J.A., The sardinas/patterson and levenstein theorems, Inform. control, 10, 120-136, (1967) · Zbl 0148.40306 [4] Sardinas, A.A.; Patterson, G.W., A necessary and sufficient condition for unique decomposition of coded message, IER conv. record, 8, 104-108, (1953) [5] Tilson, B., The intersection of free submonoids of a free monoid is free, Semigroup forum, 4, 345-350, (1972) · Zbl 0261.20060 [6] Van, D.L., Codes avec des mots infinis, RAIRO informatique théorique, 16, 371-386, (1982) · Zbl 0498.68053 [7] Van, D.L., Sous-monoïdes et codes avec des mots infinis, Semigroup forum, 26, 75-87, (1983) · Zbl 0504.68054 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.