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On the Ehrenfeucht conjecture for DOL languages. (English) Zbl 0544.68050

In this paper the Ehrenfeucht conjecture - that for every language \(L\subseteq \Sigma^*\) there exists a finite subset F of L such that for any pair of morphisms on \(\Sigma^*\), \(g(x)=h(x)\) for each x in L if and only if \(g(x)=h(x)\) for each x in F - is considered. Such a finite subset F has been called a test set for L. The notion of deviation of a string with respect to a language is introduced. Then this is used to give a sufficient condition for the existence of such a test set: ”Every language L over \(\{a_ 1,...,a_ t\}\) with bounded prefix deviation and fair distribution of letters has a test set.” Also it is proved that a test set effectively exists for each positive DOL language.
Reviewer: G.Orman

MSC:

68Q45 Formal languages and automata
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References:

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