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 , a grammar-based code transforms into a context-free grammar . The problem of finding a smallest grammar for an input sequence is known to be NP-hard, 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, variations of the incremental parsing Lempel-Ziv code, the multilevel pattern matching (MPM) algorithm, 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.
The compression programs of the following are available from external links.
- Sequitur 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 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.
- Kieffer, J. C.; Yang, E.-H. (2000), "Grammar-based codes: A new class of universal lossless source codes", IEEE Trans. Inform. 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. Inform. Theory, 51 (7): 2554–2576, doi:10.1109/tit.2005.850116
- Kieffer, J. C.; Yang, E.-H.; Nelson, G.; Cosman, P. (2000), "Universal lossless compression via multilevel pattern matching", IEEE Trans. Inform. Theory, 46 (4): 1227–1245, doi:10.1109/18.850665
- Ziv, J.; Lempel, A. (1978), "Compression of individual sequences via variable rate coding", IEEE Trans. Inform. Theory, 24 (5): 530–536, doi:10.1109/TIT.1978.1055934
- 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, hdl:10289/1186
- Larsson, N. J.; Moffat, A. (2000), "Offline Dictionary-Based Compression", IEEE, 88 (11): 1722–1732, doi:10.1109/5.892708