Pebbling mountain ranges and its application to DCFL-recognition

  • Kurt Mehlhorn
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 85)

Abstract

Recently, S.A. Cook showed that DCFL's can be recognized in O((log n)2) space and polynomial time simultaneously. We study the problem of pebbling mountain ranges (= the height of the pushdown-store as a function of time) and describe a family of pebbling strategies. One such pebbling strategy achieves a simultaneous O((log n)2/log log n) space and polynomial time bound for pebbling mountain ranges. We apply our results to DCFL recognition and show that the languages of input-driven DPDA's can be recognized in space O((log n)2/log log n). For general DCFL's we obtain a parameterized family of recognition algorithms realizing various simultaneous space and time bounds. In particular, DCFL's can be recognized in space O((log n)2) and time O(n2.87) or space O(√n log n) and time O(n1.5 log log n) or space O(n/log n) and time O(n(log n)3). More generally, our methods exhibit a general space-time tradeoff for manipulating pushdownstores (e.g. run time stack in block structured programming languages).

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References

  1. S.A. Cook: Deterministic CFL's are accepted simultaneously in polynomial time and log squared tape, 11th ACM Symposium on Theory of Computing, 1971, 338–345Google Scholar
  2. E.M. Gurari, O.H. Ibarra: On the space complexity of recursive algorithm, Inf. Proc. Letters, Vol. 8, No. 5, 1979, 267–272Google Scholar
  3. B. Schmidt: Ph.D. Thesis, Universität des Saarlandes, Fachbereich 10, 6600 Saarbrücken, in preparationGoogle Scholar
  4. S. Swami, J. Savage: Space-Time Tradeoffs for linear Recursion, 6th ACM Symposium on Principles of Programming Languages, 1979, 135–142Google Scholar

Copyright information

© Springer-Verlag 1980

Authors and Affiliations

  • Kurt Mehlhorn
    • 1
  1. 1.FB 10, Universität des SaarlandesSaarbrückenWest Germany

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