## 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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