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Disjunctive languages and compatible orders. (English) Zbl 0674.20040

Let X be an alphabet, \(2\leq | X| <\aleph_ 0\), and let \(L\subseteq X^*\). For \(u\in X^*\) let \(L..u=\{(\alpha,\beta)|\) \(\alpha,\beta \in X^*\), \(\alpha\) \(u\beta\in L\}\) be the set of contexts of u with respect to L. The language L is said to be disjunctive if the principal congruence defined by L is the equality, that is, if \(L..u=L..v\) implies \(u=v\). The authors introduce the following classification of disjunctive languages: L is s-disjunctive if L..u\(\subseteq L..v\) implies \(u=v\); it is m-disjunctive if it is disjunctive, but not s-disjunctive. Several properties of s-disjunctive and m-disjunctive languages are proved.
Reviewer: H.Jürgensen

MSC:

20M35 Semigroups in automata theory, linguistics, etc.
20M05 Free semigroups, generators and relations, word problems
68Q45 Formal languages and automata
94B60 Other types of codes
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References:

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