Bounded length UCFG equivalence

  • B. Litow
Session 6b: Invited Presentation
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1178)


A randomised polylog time algorithm is given for deciding whether or not the sets of words of a given length generated by two unambiguous context-free grammars coincide. The algorithm is in randomised NC4 in terms of the product of the grammar size and the length.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    S. Berkowitz. On computing the determinant in small parallel time using a small number of processors. Inf. Proc. Lett., 18:147–150, 1984.CrossRefGoogle Scholar
  2. 2.
    A. Bertoni, M. Goldwurm, and P. Massazza. Counting problems and algebraic formal power series in noncommuting variables. Inf. Proc. Lett., 34:117–121, 1990.CrossRefGoogle Scholar
  3. 3.
    Michael R. Garey and David S. Johnson. Computers and Intractability. W.H.Freeman and Company, New York, 1979.Google Scholar
  4. 4.
    J. Hopcroft and J. Ullman. Introduction to Automata Theory,Languages and Computation. Addison-Wesley, 1979.Google Scholar
  5. 5.
    D. Huynh. The complexity of ranking. In 3rd Structure in Complexity Theory Conf., pages 204–212, 1988.Google Scholar
  6. 6.
    D. Huynh. The complexity of deciding code and monoid properties for regular sets. Technical report, Computer science, U. Texas-Dallas, 1990.Google Scholar
  7. 7.
    D.T. Huynh. The complexity of ranking simple languages. Mathematical Systems Theory, 23:1–19, 1990.CrossRefGoogle Scholar
  8. 8.
    W. Kuich and A. Salomaa. Semirings, Automata, Languages. Springer-Verlag, 1986.Google Scholar
  9. 9.
    S. Lang. Algebra. Addison-Wesley, 1965.Google Scholar
  10. 10.
    B. Litow. Parallel complexity of the regular code problem. Inf. and Comp., 86, 1:107–114, 1990.CrossRefGoogle Scholar
  11. 11.
    B. Litow. Numbering unambiguous context-free languages. In 17th Australian Computer Society Conf., pages 373–378. University of Canterbury, New Zealand, 1994.Google Scholar
  12. 12.
    K. Mulmuley, U. Vazirani, and V. Vazirani. Matching is as easy as matrix inversion. In 19th Symp. on Theory of Computing (STOC), pages 345–354. ACM, 1987.Google Scholar
  13. 13.
    I. Wegener. The Complexity of Boolean Functions. Wiley-Teubner, 1987.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • B. Litow
    • 1
  1. 1.Dept. of Computer ScienceJames Cook UniversityAustralia

Personalised recommendations