Grammar-based code

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 x = x 1 ⋯ x n {displaystyle x=x_{1}cdots x_{n}} , a grammar-based code transforms x {displaystyle x} into a context-free grammar G {displaystyle G} .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 G {displaystyle G} is further compressed by statistical encoders like arithmetic coding. 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 x = x 1 ⋯ x n {displaystyle x=x_{1}cdots x_{n}} , a grammar-based code transforms x {displaystyle x} into a context-free grammar G {displaystyle G} .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 G {displaystyle G} is further compressed by statistical encoders like arithmetic coding. 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.