Polynomial time and space shift-reduce parsing of arbitrary context-free grammars

Abstract

We introduce an algorithm for designing a predictive left to right shift-reduce non-deterministic push-down machine corresponding to an arbitrary unrestricted context-free grammar and an algorithm for efficiently driving this machine in pseudo-parallel. The performance of the resulting parser is formally proven to be superior to Earley's parser (1970). The technique employed consists in constructing before run-time a parsing table that encodes a non-deterministic machine in the which the predictive behavior has been compiled out. At run time, the machine is driven in pseudo-parallel with the help of a chart. The recognizer behaves in the worst case in O(IGI2n3)-time and O(IGIn2)-space. However in practice it is always superior to Earley's parser since the prediction steps have been compiled before run-time. Finally, we explain how other more efficient variants of the basic parser can be obtained by determinizing portionsof the basic non-deterministic pushdown machine while still using the same pseudo-parallel driver.