Advertisement

Models of Pushdown Automata with Reset

  • Nuri Taşdemi̇r
  • A. C. Cem Say
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6795)

Abstract

We examine various pushdown automaton variants that are architecturally intermediate between the one-way PDA and the two-way PDA (2PDA), where leftward moves of the input head can only reset it to the left end of the tape, and some component of the machine configuration may be “forgotten”, that is, reset to its initial value, whenever such a move is performed. Most of these model variants are shown to be equivalent in power to either the 2PDA or the one-way PDA. One exception is the Resettable Pushdown Automaton (RPDA), where the stack contents are lost every time the input is reset, and which we prove to be intermediate in power between the PDA and the 2PDA. We give full characterizations of the classes of languages recognized by both the deterministic and the nondeterministic versions of the RPDA.

Keywords

automata and formal languages two-way PDAs 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Freivalds, R., Karpinski, M.: Lower space bounds for randomized computation. In: ICALP 1994, pp. 580–592 (1994)Google Scholar
  2. 2.
    Golovkins, M.: Quantum pushdown automata. In: Jeffery, K., Hlaváč, V., Wiedermann, J. (eds.) SOFSEM 2000. LNCS, vol. 1963, pp. 336–346. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  3. 3.
    Gray, J.N., Harrison, M.A., Ibarra, O.H.: Two-way pushdown automata. Information and Control 11(1-2), 30–70 (1967)Google Scholar
  4. 4.
    Hoogeboom, H.J., Engelfriet, J.: Pushdown automata. In: Formal Languages and Applications. SFSC, ch. 6, vol. 148, pp. 117–138. Springer, Berlin (2004)Google Scholar
  5. 5.
    Hopcroft, J.E., Ullman, J.D.: Formal languages and their relation to automata. Addison-Wesley Longman Publishing Co., Boston (1969)zbMATHGoogle Scholar
  6. 6.
    Hromkovic, J., Schnitger, G.: On probabilistic pushdown automata. Information and Computation 208(8), 982–995 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Jančar, P., Mráz, F., Plátek, M., Procházka, M., Vogel, J.: Deleting automata with a restart operation. In: Bozapalidis, S. (ed.) Proceedings of DLT 1997, Greece, pp. 191–202 (1997)Google Scholar
  8. 8.
    Jančar, P., Mráz, F., Plátek, M., Vogel, J.: Restarting automata. LNCS, vol. 965, pp. 283–292 (1995)Google Scholar
  9. 9.
    Liu, L.Y., Weiner, P.: An infinite hierarchy of intersections of context-free languages. Mathematical Systems Theory 7, 185–192 (1973)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Okhotin, A.: Conjunctive grammars. J. A. Lang. Comb. 6, 519–535 (2001)MathSciNetzbMATHGoogle Scholar
  11. 11.
    Shepherdson, J.C.: The reduction of two-way automata to one-way automata. IBM Journal of Research and Development 3, 198–200 (1959)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Stearns, R.E., Hartmanis, J., Lewis II, P.M.: Hierarchies of memory limited computations. In: SWCT 1965, pp. 179–190 (1965)Google Scholar
  13. 13.
    Szepietowski, A.: Turing Machines with Sublogarithmic Space. Springer, Heidelberg (1994)CrossRefzbMATHGoogle Scholar
  14. 14.
    Wotschke, D.: Nondeterminism and boolean operations in PDA’s. Journal of Computer and System Sciences 16, 456–461 (1978)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Yakaryılmaz, A., Cem Say, A.C.: Succinctness of two-way probabilistic and quantum finite automata. DMTCS 12(4), 19–40 (2010)MathSciNetzbMATHGoogle Scholar
  16. 16.
    Yakaryılmaz, A., Cem Say, A.C.: Unbounded-error quantum computation with small space bounds. Technical Report arXiv:1007.3624 (2010)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Nuri Taşdemi̇r
    • 1
  • A. C. Cem Say
    • 1
  1. 1.Department of Computer EngineeringBoğaziçi UniversityBebekTurkey

Personalised recommendations