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Grammar-based codes or Grammar-based compression are compression algorithms based on the idea of constructing a context-free grammar (CFG) for the string to be compressed. Examples include universal lossless data compression algorithms.[1] To compress a data sequence , a grammar-based code transforms into a context-free grammar .
The problem of finding a smallest grammar for an input sequence (smallest grammar problem) is known to be NP-hard,[2] so many grammar-transform algorithms are proposed from theoretical and practical viewpoints.
Generally, the produced grammar is further compressed by statistical encoders like arithmetic coding.
Examples and characteristics
The class of grammar-based codes is very broad. It includes block codes, the multilevel pattern matching (MPM) algorithm,[3] variations of the incremental parsing Lempel-Ziv code,[4] and many other new universal lossless compression algorithms.
Grammar-based codes are universal in the sense that they can achieve asymptotically the entropy rate of any stationary, ergodic source with a finite alphabet.
Practical algorithms
The compression programs of the following are available from external links.
Sequitur[5] is a classical grammar compression algorithm that sequentially translates an input text into a CFG, and then the produced CFG is encoded by an arithmetic coder.
Re-Pair[6] is a greedy algorithm using the strategy of most-frequent-first substitution. The compressive performance is powerful, although the main memory space requirement is very large.
GLZA,[7] which constructs a grammar that may be reducible, i.e., contain repeats, where the entropy-coding cost of "spelling out" the repeats is less than the cost creating and entropy-coding a rule to capture them. (In general, the compression-optimal SLG is not irreducible, and the Smallest Grammar Problem is different from the actual SLG compression problem.)
^Kieffer, J. C.; Yang, E.-H. (2000), "Grammar-based codes: A new class of universal lossless source codes", IEEE Trans. Inf. Theory, 46 (3): 737–754, doi:10.1109/18.841160
^Charikar, M.; Lehman, E.; Liu, D.; Panigrahy, R.; Prabharakan, M.; Sahai, A.; Shelat, A. (2005), "The Smallest Grammar Problem", IEEE Trans. Inf. Theory, 51 (7): 2554–2576, doi:10.1109/tit.2005.850116, S2CID6900082
^Nevill-Manning, C. G.; Witten, I. H. (1997), "Identifying Hierarchical Structure in Sequences: A linear-time algorithm", Journal of Artificial Intelligence Research, 7 (4): 67–82, arXiv:cs/9709102, doi:10.1613/jair.374, hdl:10289/1186, S2CID2957960
^Conrad, Kennon J.; Wilson, Paul R. (2016). "Grammatical Ziv-Lempel Compression: Achieving PPM-Class Text Compression Ratios with LZ-Class Decompression Speed". 2016 Data Compression Conference (DCC). p. 586. doi:10.1109/DCC.2016.119. ISBN978-1-5090-1853-6. S2CID3116024.
This page was last edited on 8 August 2023, at 22:09