On Context-Free Languages of Scattered Words

Abstract

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 Muller context-free language (MCFL). In the first part of the paper, we prove that an MCFL of scattered words is a BCFL iff the rank of every word in the language is bounded by an integer depending only on the language.Then we establish operational characterizations of the BCFLs of well-ordered and scattered words. We prove that a language is a BCFL consisting of well-ordered words iff it can be generated from the singleton languages containing the letters of the alphabet by substitution into ordinary context-free languages and the ω-power operation. We also establish a corresponding result for BCFLs of scattered words and define expressions denoting BCFLs of well-ordered and scattered words. In the final part of the paper we give some applications.

Operational characterization of scattered MCFLs -- Technical Report

“…A Kleene-type characterization of BCFLs of well-ordered and scattered words was given in [16]. Here we provide a Kleene-type characterization of MCFLs of well-ordered and scattered words.…”

“…It was shown in [16] that the syntactic fragment of the above expressions, with the ω-power operation restricted to closed expressions, characterizes the BCFLs of well-ordered words. A similar, but more involved result holds for MCFLs of scattered words, cf.…”