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A representation of recursively enumerable languages by two homomorphisms and a quotient. (English) Zbl 0664.68075
For two strings x and y, $$x\setminus y$$ is the string z when $$y=xz$$; otherwise $$x\setminus y$$ is undefined. The author proves the following representation theorem: For each recursively enumerable set L (over alphabet $$\Sigma)$$ there exist two homomorphisms $$h_ 1$$, $$h_ 2:$$ $$\Sigma^*_ 1\to \Sigma^*_ 2$$ $$(\Sigma \subseteq \Sigma_ 2)$$ such that for every $$w\in \Sigma^*$$, $$w\in L$$ if and only if $$w=h_ 1(x)\setminus h_ 2(x)$$ for some $$x\in \Sigma^*_ 1.$$
The author discusses some complexity issues related to this representation and also some variants of the representation result.
Reviewer: G.Slutzki

##### MSC:
 68Q45 Formal languages and automata
Full Text:
##### References:
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