Space and time efficient simulations and characterizations of some restricted classes of PDAS

  • Oscar H. Ibarra
  • Sam M. Kim
  • Louis E. Rosier
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 172)


In this paper we present some space/time efficient Turing machine algorithms for recognizing some subclasses of DCFL's. In particular, we show that the finite minimal stacking and “simple” strict restricted (a subclass of strict restricted) deterministic pushdown automata (FMS-DPDA's SSR-DPDA's, respectively) can be simulated by offline Turing machines simultaneously in space S(n) and time n2/S(n) for any tape function S(n) satisfying log n ≤ S(n) ≤ n which is constructable in n2/S(n) time. Related techniques can be used to give interesting characterizations of 2-head 2-way finite automata, both deterministic and nondeterministic. In particular we show that a 2-head 2-way deterministic finite automataton is equivalent to a simple type of 2-way deterministic checking stack automaton. This is in contrast to a result which shows that 2-way nondeterministic checking stack automata are equivalent to nondeterministic linear bounded automata. We also show that a language L is accepted by a 2k-head two-way nondetermistic finite automaton if and only if it is accepted by a k-head two-way nondeterministic pushdown automaton which makes at most one reversal on its stack.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1).
    Braunmuhl, B. and Verbeek, R., A recognition algorithm for deterministic CFLs optimal in time and space, Proc. 21st IEEE-FOCS, pp. 411–420 (1980).Google Scholar
  2. 2).
    Cook, S., An observation on time-storage tradeoff, JCSS, Vol. 9, pp. 308–316 (1974).Google Scholar
  3. 3).
    Cook, S., Deterministic CFL's are accepted simultaneously in polynomial time and log squared space, Proc. 11th ACM Symp. on Theory of Comp., pp. 338–345 (1979).Google Scholar
  4. 4).
    Fischer, P., Meyer, A. and Rosenberg, A., Counter machines and counter languages, MST, Vol. 2, No. 3, pp. 265–283 (1968).Google Scholar
  5. 5).
    Galil, Z., Two-way deterministic pushdown automaton languages and some open problems in the theory of computing, MST, Vol. 10, pp. 211–228 (1977).Google Scholar
  6. 6).
    Ginsburg, S. and Harrison, M., Backeted context-free languages, JCSS, Vol. 1, pp. 1–23 (1967).Google Scholar
  7. 7).
    Greibach, S., Checking automata and one-way stack languages, JCSS, Vol. 3, pp. 196–217 (1969).Google Scholar
  8. 8).
    Gurari, E. and Ibarra, O., Path systems: constructions, solutions and applications, SIAM J. Comput., Vol. 9, No. 2, pp. 348–374 (1980).Google Scholar
  9. 9).
    Hopcraft, J. and Ullman, J., Unified theory of automata, The Bell System Technical J., Vol. 46, No. 8, pp. 1793–1829 (1967).Google Scholar
  10. 10).
    Ibarra, Q., Characterizations of some tape and time complexity classes of Turing Machines in terms of multihead and auxiliary stack automata, JCSS, Vol. 5, No. 2, pp. 88–117 (1971).Google Scholar
  11. 11).
    Ibarra, O., On two-way multihead automata, JCSS, Vol. 7, pp. 28–36 (1973).Google Scholar
  12. 12).
    Igarashi, Y., Tape bounds for some subclasses of deterministic context-free languages, Information and Control, Vol. 37, pp. 321–333 (1978).Google Scholar
  13. 13).
    Igarashi, Y., The tape complexity of some classes of Szilard languages, SIAM J. Comput., Vol. 6, No. 3, pp. 461–466 (1977).Google Scholar
  14. 14).
    Lewis, P., Hartmanis, J., and Stearns, R., Memory bounds for the recognition of context-free and context-sensitive languages, IEEE Conf. Record on Switching Circuit Theory and Logic Design, pp. 191–202 (1965).Google Scholar
  15. 15).
    Lipton, R. and Zalcstein, Y., Word problems solvable in logspace, Computer Science Department, Yale University, Tech. Report #6 (1976).Google Scholar
  16. 16).
    Lynch, N., Logspace recognition and translation of parenthesis languages, JACM, Vol. 24, No. 4, pp. 583–590 (1977).Google Scholar
  17. 17).
    Mehlhorn, K., Bracket-languages are recognizable in logarithmic space, Information Processing Letters, Vol. 5, No. 6, pp. 168–170 (1976).Google Scholar
  18. 18).
    Moriya, E., Associate languages and derivational complexity of formal grammars and languages, Information and Control, Vol. 22, pp. 139–162 (1973).Google Scholar
  19. 19).
    Richie, R. and Springsteel, F., Language recognition by marking automata, Information and Control, Vol. 20, pp. 313–330 (1972).Google Scholar
  20. 20).
    Sudborough, I., A note on tape-bounded complexity classes and linear context-free languages, JACM, Vol. 22, No. 4, pp. 499–500 (1975).Google Scholar
  21. 21).
    Sudborough, I., On tape-bounded complexity classes and multihead finite automata, JCSS, 10, pp. 338–345 (1979).Google Scholar
  22. 22).
    Sudborough, I., On deterministic context-free languages, multihead automata, and the power of an auxiliary pushdown store, 8th Annual ACM Symp. on Theory of Computing, pp. 141–148 (1976).Google Scholar
  23. 23).
    Valiant, L., Decision problems for families of deterministic pushdown automata, Ph.D. thesis, University of Warwick, U.K. (1973).Google Scholar
  24. 24).
    Verbeek, R., Time-space trade-offs for general recursion, Proc. 22nd IEEE-FOCS, pp. 228–234 (1981).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1984

Authors and Affiliations

  • Oscar H. Ibarra
    • 1
  • Sam M. Kim
    • 2
  • Louis E. Rosier
    • 3
  1. 1.Department of Computer ScienceUniversity of MinnesotaMinneapolis
  2. 2.Department of Mathematical SciencesRensselaer Polytechnic InstituteTroy
  3. 3.Department of Computer SciencesUniversity of TexasAustin

Personalised recommendations