Text Compression Using Abstract Numeration System on a Regular Language

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.