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A syntactic congruence for rational $$\omega$$-languages. (English) Zbl 0578.68057
Summary: Büchi has proved that if L is a rational $$\omega$$-language, then there exists a finite congruence for which L is saturated in the following sense: $$[u][v]^{\omega}\cap L\neq \emptyset \Rightarrow [u][v]^{\omega}\subset L$$. Here, we define the syntactic congruence of L, which is the largest congruence having this property.

##### MSC:
 68Q45 Formal languages and automata
##### Keywords:
rational language; omega-language
Full Text:
##### References:
 [1] Berstel, J., Transductions and context-free languages, (1979), Teubner Stuttgart · Zbl 0424.68040 [2] Büchi, J.R., On a decision method in restricted second order arithmetic, (), 1-11 · Zbl 0147.25103 [3] Eilenberg, S., () [4] Schützenberger, M.P., A propos des relations rationnelles fonctionnelles, (), 103-114
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