RePair Grammars Are the Smallest Grammars for Fibonacci Words

Takuya Mieno, Shunsuke Inenaga, Takashi Horiyama

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Grammar-based compression is a loss-less data compression scheme that represents a given string w by a context-free grammar that generates only w. While computing the smallest grammar which generates a given string w is NP-hard in general, a number of polynomial-time grammar-based compressors which work well in practice have been proposed. RePair, proposed by Larsson and Moffat in 1999, is a grammar-based compressor which recursively replaces all possible occurrences of a most frequently occurring bigrams in the string. Since there can be multiple choices of the most frequent bigrams to replace, different implementations of RePair can result in different grammars. In this paper, we show that the smallest grammars generating the Fibonacci words Fk can be completely characterized by RePair, where Fk denotes the k-th Fibonacci word. Namely, all grammars for Fk generated by any implementation of RePair are the smallest grammars for Fk, and no other grammars can be the smallest for Fk. To the best of our knowledge, Fibonacci words are the first non-trivial infinite family of strings for which RePair is optimal.

Original languageEnglish
Title of host publication33rd Annual Symposium on Combinatorial Pattern Matching, CPM 2022
EditorsHideo Bannai, Jan Holub
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959772341
DOIs
Publication statusPublished - Jun 1 2022
Event33rd Annual Symposium on Combinatorial Pattern Matching, CPM 2022 - Prague, Czech Republic
Duration: Jun 27 2022Jun 29 2022

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume223
ISSN (Print)1868-8969

Conference

Conference33rd Annual Symposium on Combinatorial Pattern Matching, CPM 2022
Country/TerritoryCzech Republic
CityPrague
Period6/27/226/29/22

All Science Journal Classification (ASJC) codes

  • Software

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