On context-free languages of scattered words
Abstract
It is known that if a B\"uchi context-free language (BCFL) consists of scattered words, then there is an integer , depending only on the language, such that the Hausdorff rank of each word in the language is bounded by . Every BCFL is a M\"uller 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 -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.
Keywords
Cite
@article{arxiv.1111.3439,
title = {On context-free languages of scattered words},
author = {Zoltan Esik and Satoshi Okawa},
journal= {arXiv preprint arXiv:1111.3439},
year = {2015}
}