Grammar-based code
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. To compress a data sequence x = x 1 ⋯ x n {\displaystyle x=x_{1}\cdots x_{n}} , a grammar-based code transforms x {\displaystyle x} into a context-free grammar G {\displaystyle G} . The problem of finding a smallest grammar for an input sequence (smallest grammar problem) is known to be NP-hard, so many grammar-transform algorithms are proposed from theoretical and practical viewpoints. Generally, the produced grammar G {\displaystyle G} is further compressed by statistical encoders like arithmetic coding.
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
[edit]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
[edit]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.)
See also
[edit]References
[edit]- ^ 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, S2CID 6900082
- ^ Kieffer, J. C.; Yang, E.-H.; Nelson, G.; Cosman, P. (2000), "Universal lossless compression via multilevel pattern matching", IEEE Trans. Inf. Theory, 46 (4): 1227–1245, doi:10.1109/18.850665, S2CID 8191526
- ^ Ziv, J.; Lempel, A. (1978), "Compression of individual sequences via variable rate coding", IEEE Trans. Inf. Theory, 24 (5): 530–536, doi:10.1109/TIT.1978.1055934, hdl:10338.dmlcz/142945
- ^ 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, S2CID 2957960
{{citation}}: CS1 maint: unflagged free DOI (link) - ^ Larsson, N. J.; Moffat, A. (2000), "Offline Dictionary-Based Compression" (PDF), Proceedings of the IEEE, 88 (11): 1722–1732, doi:10.1109/5.892708
- ^ 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. ISBN 978-1-5090-1853-6. S2CID 3116024.
External links
[edit]- GLZA discussion and paper
- Description of grammar-based codes with example
- Sequitur codes Archived 2008-10-13 at the Wayback Machine
- Re-Pair codes
- Re-Pair codes a version of Gonzalo Navarro.
- GrammarViz 2.0 - implementation of Sequitur, Re-Pair, and parallel Re-Pair in Java.