Earley parser

Earley parser

Class	Parsing grammars that are context-free
Data structure	String
Worst-case performance	${\displaystyle O(n^{3})}$
Best-case performance	${\displaystyle \Omega (n)}$ for all deterministic context-free grammars ${\displaystyle \Omega (n^{2})}$ for unambiguous grammars
Average performance	${\displaystyle \Theta (n^{3})}$

In computer science, the Earley parser is an algorithm for parsing strings that belong to a given context-free language, though (depending on the variant) it may suffer problems with certain nullable grammars.^[1] The algorithm, named after its inventor, Jay Earley, is a chart parser that uses dynamic programming; it is mainly used for parsing in computational linguistics. It was first introduced in his dissertation^[2] in 1968 (and later appeared in an abbreviated, more legible, form in a journal^[3]).

Earley parsers are appealing because they can parse all context-free languages, unlike LR parsers and LL parsers, which are more typically used in compilers but which can only handle restricted classes of languages. The Earley parser executes in cubic time in the general case ${\displaystyle {O}(n^{3})}$, where n is the length of the parsed string, quadratic time for unambiguous grammars ${\displaystyle {O}(n^{2})}$,^[4] and linear time for all deterministic context-free grammars. It performs particularly well when the rules are written left-recursively.