Grammar-based codes or grammar-based compression are

compression Compression may refer to: Physical science *Compression (physics), size reduction due to forces *Compression member, a structural element such as a column *Compressibility, susceptibility to compression * Gas compression *Compression ratio, of a ...

algorithms based on the idea of constructing a

context-free grammar In formal language theory, a context-free grammar (CFG) is a formal grammar whose production rules can be applied to a nonterminal symbol regardless of its context. In particular, in a context-free grammar, each production rule is of the fo ...

(CFG) for the string to be compressed. Examples include universal

lossless data compression Lossless compression is a class of data compression that allows the original data to be perfectly reconstructed from the compressed data with no loss of information. Lossless compression is possible because most real-world data exhibits Redundanc ...

algorithms. To compress a data sequence

x = x_1 \cdots x_n

, a grammar-based code transforms

x

into a context-free grammar

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

is further compressed by statistical encoders like

arithmetic coding Arithmetic coding (AC) is a form of entropy encoding used in lossless data compression. Normally, a String (computer science), string of characters is represented using a fixed number of bits per character, as in the American Standard Code for In ...

Examples and characteristics

The class of grammar-based codes is very broad. It includes

block code In coding theory, block codes are a large and important family of Channel coding, error-correcting codes that encode data in blocks. There is a vast number of examples for block codes, many of which have a wide range of practical applications. Th ...

s, the multilevel pattern matching (MPM) 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 In the mathematical theory of probability, the entropy rate or source information rate is a function assigning an entropy to a stochastic process. For a strongly stationary process, the conditional entropy for latest random variable eventually ...

of any stationary,

ergodic In mathematics, ergodicity expresses the idea that a point of a moving system, either a dynamical system or a stochastic process, will eventually visit all parts of the space that the system moves in, in a uniform and random sense. This implies th ...

source with a finite alphabet.

Practical algorithms

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 Re-Pair (short for recursive pairing) is a grammar-based compression algorithm that, given an input text, builds a straight-line program, i.e. a context-free grammar In formal language theory, a context-free grammar (CFG) is a formal gramm ...

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. (In general, the compression-optimal SLG is not irreducible, and the Smallest Grammar Problem is different from the actual SLG compression problem.)

References

External links

GLZA discussion and paperDescription of grammar-based codes with exampleSequitur codes

a version of Gonzalo Navarro.
GrammarViz 2.0
- implementation of Sequitur, Re-Pair, and parallel Re-Pair in Java. {{Compression methods Data compression Coding theory Information theory

Examples and characteristics

Practical algorithms

See also

References

External links