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This is an old revision of this page, as edited by 2602:306:cd5b:fd30:61c0:3b3e:902:22a7 (talk) at 01:41, 3 December 2017 (Smallest Grammar Problem isn't just intractable, it's not the real SLG compression problem (which must take entropy coding into account)). The present address (URL) is a permanent link to this revision, which may differ significantly from the current revision.
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I will update the article on grammar-based coding from time to time -- Da-ke.

Article needs to be updated with references about Structured Grammar Based Codes. Amanbhatia 05:34, 11 August 2008 (UTC)[reply]

The problem of constructing the "smallest grammar" isn't just intractable... for understanding data compression with entropy coding, it's the wrong problem. The compression-optimal SLG is generally not irreducible, because you may have patterns that repeat infrequently but are made of very frequently-repeating constituents whose entropy codes are therefore short. In such cases, it's worth "spelling out" each repeat in terms of the (short codes for) the constituents, rather than paying the cost of encoding the repeating pattern as a separate rule. See Conrad and Wilson (GLZA) on this.