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It is known that if a Büchi context-free language (BCFL) consists of scattered words, then there is an integer n, depending only on the language, such that the Hausdorff rank of each word in the language is bounded by n. Every BCFL is a Müller context-free language (MCFL). In the first part of the paper, we prove that an MCFL of scattered words is a BCFL(More)