Text Compression using Abstract Numeration System on a Regular Language
arXiv:1308.0267
Abstract
An abstract numeration system (ANS) is a numeration system that provides a one-to-one correspondence between the natural numbers and a regular language. In this paper, we define an ANS-based compression as an extension of this correspondence. In addition, we show the following results: 1) an average compression ratio is computable from a language, 2) an ANS-based compression runs in sublinear time with respect to the length of the input string, and 3) an ANS-based compression can be extended to block-based compression using a factorial language.
An extended abstract of the accepted paper for JSSST Journal "Computer Software" (Japanese, available at http://www.shudo.is.titech.ac.jp/members/sinya)