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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 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.