RePair Grammars are the Smallest Grammars for Fibonacci Words
| Autor: | Mieno, Takuya, Inenaga, Shunsuke, Horiyama, Takashi |
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| Rok vydání: | 2022 |
| Předmět: |
grammar based compression
FOS: Computer and information sciences Fibonacci words TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES Discrete Mathematics (cs.DM) Mathematics of computing → Combinatorics on words smallest grammar problem FOS: Mathematics Mathematics - Combinatorics Combinatorics (math.CO) Computer Science - Discrete Mathematics RePair |
| DOI: | 10.48550/arxiv.2202.08447 |
| Popis: | 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 F_k can be completely characterized by RePair, where F_k denotes the k-th Fibonacci word. Namely, all grammars for F_k generated by any implementation of RePair are the smallest grammars for F_k, and no other grammars can be the smallest for F_k. To the best of our knowledge, Fibonacci words are the first non-trivial infinite family of strings for which RePair is optimal. LIPIcs, Vol. 223, 33rd Annual Symposium on Combinatorial Pattern Matching (CPM 2022), pages 26:1-26:17 |
| Databáze: | OpenAIRE |
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