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A grammar compression is a context-free grammar (CFG) deriving a single string deterministically. For an input string of length N over an alphabet of size σ, the smallest CFG is O(lg N )approximable in the offline setting and O(lg N lg * N )-approximable in the online setting. In addition, an information-theoretic lower bound for representing a CFG in Chomsky normal form of n variables is lg(n!/n σ ) + n + o(n) bits. Although there is an online grammar compression algorithm that directlydoi:10.4230/lipics.esa.2017.67 dblp:conf/esa/TakabatakeIS17 fatcat:chxvgfhnyvalnlzoigvtma7dvu