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A parsing algorithm which seems to be the most efficient general context-free algorithm known is described. It is similar to both Knuth's LR( k ) algorithm and the familiar top-down algorithm. It has a time bound proportional to n 3 (where n is the length of the string being parsed) in general; it has an n 2 bound for unambiguous grammars; and it runs in linear time on a large class of grammars, which seems to include most practical context-free programming language grammars. In an empirical comparison it appears to be superior to the top-down and bottom-up algorithms studied by Griffiths and Petrick.
Jay Earley (Sun,) studied this question.