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

  • Authors:
  • Yves Schabes

  • Affiliations:
  • University of Pennsylvania, Philadelphia, PA

  • Venue:
  • ACL '91 Proceedings of the 29th annual meeting on Association for Computational Linguistics
  • Year:
  • 1991

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Abstract

We introduce an algorithm for designing a predictive left to right shift-reduce non-determinisic 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(|G|2n3)-time and O(|G|n2)-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 portions of the basic non-deterministic push-down machine while still using the same pseudo-parallel driver.