Grammar-based code

Grammar-based codes or grammar-based compression are compression algorithms based on the idea of constructing a context-free grammar 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, the multilevel pattern matching algorithm, variations of the incremental parsing Lempel-Ziv code, 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.
GLZA, 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.