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Unambiguous simulations of auxiliary pushdown automata and circuits

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LATIN '92 (LATIN 1992)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 583))

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Abstract

A simulation ‘free of cost’ of polynomially ambiguity bounded AuxPDAs by unambiguous ones is given. From this it follows that context free languages (CFLs) of polynomial ambiguity can be recognized as efficiently by unambiguous auxiliary pushdown automata (AuxPDAs) as unambiguous CFLs (UCFLs). Furthermore, a first nontrivial upper bound for a circuit class defined by Lange and its closure under complementation are indicated. Finally, normal forms for AuxPDAs are investigated; inter alia it is shown that several kinds of AuxPDAs can be made oblivious, i.e., the movements of all heads are independent from the input.

This research was partially supported by the Deutsche Forschungsgemeinschaft, SFB 342, Teilprojekt A4 “KLARA”

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References

  1. M. Ajtai, J. Komlós, and E. Szemerédi. Sorting in c log n parallel steps. Combinatorica, 3:1–19, 1983.

    Google Scholar 

  2. C. Àlvarez and B. Jenner. A very hard log space counting class. In Proc. of 5th Conference on Structure in Complexity Theory, pages 154–168, 1990. (To appear in a Special Issue of Theoretical Computer Science).

    Google Scholar 

  3. A. Borodin, S. A. Cook, P. W. Dymond, W. L. Ruzzo, and M. Tompa. Two applications of inductive counting for complementation problems. SIAM J. Comput., 18(3):559–578, 1989.

    Google Scholar 

  4. G. Buntrock, L. A. Hemachandra, and D. Siefkes. Using inductive counting to simulate nondeterministic computation. In Proc. of 15th MFCS, number 452 in LNCS, pages 187–194. Springer, 1990. (to appear in Information and Computation).

    Google Scholar 

  5. G. Buntrock, B. Jenner, K.-J. Lange, and P. Rossmanith. Unambiguity and fewness for logarithmic space. In Proc. of the 8th Conference on Fundamentals of Computation Theory, number 529 in LNCS, pages 168–179, 1991.

    Google Scholar 

  6. A. K. Chandra, D. Kozen, and L. Stockmeyer. Alternation. J. ACM, 28:114–133, 1981.

    Google Scholar 

  7. S. A. Cook. Characterizations of pushdown machines in terms of time-bounded computers. J. ACM, 18:4–18, 1971.

    Google Scholar 

  8. P. Dymond and W. L. Ruzzo. Parallel RAMs with owned global memory and deterministic language recognition. In Proc. of 13th ICALP, number 226 in LNCS, pages 95–104. Springer, 1986.

    Google Scholar 

  9. S. Fortune and J. Willie. Parallelism in random access machines. In Proc. of 10th STOC, pages 114–118, 1978.

    Google Scholar 

  10. L. M. Goldschlager. A universal interconnection pattern for parallel computers. J. ACM, 29(3):1073–1086, 1982.

    Google Scholar 

  11. T. Hagerup and T. Radzig. Every robust CRCW PRAM can efficiently simulate a PRIORITY PRAM. In Proc. of 2nd SPAA, pages 117–124, 1990.

    Google Scholar 

  12. J. E. Hopcroft and J. D. Ullman. Introduction to Automata Theory, Languages and Computation. Addison-Wesley, 1979.

    Google Scholar 

  13. K.-J. Lange. Unambiguity of circuits. In Proc. of 5th Conference on Structure in Complexity Theory, pages 130–137, 1990. (to appear in TCS).

    Google Scholar 

  14. K.-J. Lange and P. Rossmanith. Characterizing unambiguous augmented pushdown automata by circuits. In Proc. of 15th MFCS, number 452 in LNCS, pages 399–406. Springer, 1990.

    Google Scholar 

  15. P. Rossmanith, and W. Rytter. Observations on log(n) time parallel recognition of unambiguous context-free languages. Nov. 1991.

    Google Scholar 

  16. R. Niedermeier and P. Rossmanith. Unambiguous Simulations of Auxiliary Pushdown Automata and Circuits. SFB-Bericht 342/31/90 A, I9054, Institut für Informatik, Technische Universität München, Dec. 1990.

    Google Scholar 

  17. I. Parberry. Parallel Complexity Theory. Pitman, 1987.

    Google Scholar 

  18. W. L. Ruzzo. Tree-size bounded alternation. J. Comput. Syst. Sci., 21:218–235, 1980.

    Google Scholar 

  19. W. L. Ruzzo. On uniform circuit complexity. J. Comput. Syst. Sci., 22:365–383, 1981.

    Google Scholar 

  20. W. Rytter. Parallel time O(log n) recognition of unambiguous context-free languages. Inform. and Comp., 73:75–86, 1987.

    Google Scholar 

  21. I. H. Sudborough. On the tape complexity of deterministic context-free languages. J. ACM, 25:405–414, 1978.

    Google Scholar 

  22. L. Valiant. The relative complexity of checking and evaluating. Inform. Proc. Letters, 5:20–23, 1976.

    Google Scholar 

  23. H. Venkateswaran. Properties that characterize LOGCFL. J. Comput. Syst. Sci., 43:380–404, 1991.

    Google Scholar 

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Imre Simon

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© 1992 Springer-Verlag Berlin Heidelberg

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Niedermeier, R., Rossmanith, P. (1992). Unambiguous simulations of auxiliary pushdown automata and circuits. In: Simon, I. (eds) LATIN '92. LATIN 1992. Lecture Notes in Computer Science, vol 583. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0023843

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  • DOI: https://doi.org/10.1007/BFb0023843

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  • Print ISBN: 978-3-540-55284-0

  • Online ISBN: 978-3-540-47012-0

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