Grammar-based code

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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] and SEQUITUR, among others. To compress a data sequence x = x_1 \cdots x_n, a grammar-based code transforms x into a context-free CFG G. The problem to find a smallest grammar for an input sequence is known to be NP-hard,[2] so many grammar-transform algorithms are proposed from theoretical and practical viewpoints. Generally, the produced grammar G 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, variations of the incremental parsing Lempel-Ziv code,[3] the multilevel pattern matching (MPM) algorithm,[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 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 by the strategy of most-frequent-first substitution. The compressive performance is powerful, although the main memory space is very large.

See also[edit]

References[edit]

  1. ^ 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 
  2. ^ Charikar, M.; Lehman, E.; Liu, D.; Panigrapy, R.; Prabharakan, M.; Sahai, A.; Shelat, A. (2005), "The Smallest Grammar Problem", IEEE Trans. Inform. Theory 51 (7): 2554–2576 
  3. ^ 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 
  4. ^ 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 
  5. ^ 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 
  6. ^ Larsson, N. J.; Moffat, A. (2000), "Offline Dictionary-Based Compression", IEEE 88 (11): 1722–1732 

External links[edit]