Abstract
We define context-free grammars with Müller acceptance condition that generate languages of countable words. We establish several elementary properties of the class of Müller context-free languages including closure properties and others. We show that every Müller context-free grammar can be transformed into a normal form grammar in polynomial space, and then we show that many decision problems can be decided in polynomial time for Müller context-free grammars in normal form. These decision problems include deciding whether the language generated by a normal form grammar contains only well-ordered, scattered, or dense words. In a further result, we establish a limitedness property of Müller context-free grammars: if the language generated by a grammar contains only scattered words, then either there is an integer n such that each word of the language has Hausdorff rank at most n , or the language contains scattered words of arbitrarily large Hausdorff rank. We also show that it is decidable which of the two cases applies.
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