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Concept
Earley parser
Summary
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. 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 in 1968 (and later appeared in an abbreviated, more legible, form in a journal).
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 , where n is the length of the parsed string, quadratic time for unambiguous grammars , and linear time for all deterministic context-free grammars. It performs particularly well when the rules are written left-recursively.
The following algorithm describes the Earley recogniser. The recogniser can be modified to create a parse tree as it recognises, and in that way can be turned into a parser.
In the following descriptions, α, β, and γ represent any string of terminals/nonterminals (including the empty string), X and Y represent single nonterminals, and a represents a terminal symbol.
Earley's algorithm is a top-down dynamic programming algorithm. In the following, we use Earley's dot notation: given a production X → αβ, the notation X → α • β represents a condition in which α has already been parsed and β is expected.
Input position 0 is the position prior to input. Input position n is the position after accepting the nth token. (Informally, input positions can be thought of as locations at token boundaries.) For every input position, the parser generates a state set.
Official source
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