Advertisement

The simulation of two-dimensional one-marker automata by three-way turing machines

  • Akira Ito
  • Katsushi Inoue
  • Itsuo Takanami
Chapter 2 Machines
Part of the Lecture Notes in Computer Science book series (LNCS, volume 381)

Abstract

We denote a two-dimensional deterministic (nondeterministic) one-marker automaton by "2-DM1" ("2-NM1"), and a three-way two-dimensional deterministic (nondeterministic) Turing machine by "TR2-DTM" ("TR2-NTM"). In this paper, we show that the necessary and sufficient space for TR2-NTM's to simulate 2-DM1's (2-NM1's) is nlogn (n2), and the necessary and sufficient space for TR2-DTM's to simulate 2-DM1's (2-NM1's) is 2o(nlogn) (2o(n2)), where n is the number of columns of rectangular input tapes.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    M.Blum and C.Hewitt, Automata on a 2-dimensional Tape, Proceedings of the 8th IEEE symposium of Switching and Automata Theory, pp.155–160 (1967).Google Scholar
  2. [2]
    A.Rosenfeld, Picture Languages — Formal models for Picture Recognition, Academic Press (1979).Google Scholar
  3. [3]
    K. Inoue and A. Nakamura, Some Properties of Two-Dimensional Nondeterministic Finite Automata and Parallel Sequential Array Acceptors, The Transactions of the Institute of Electronics and Communication Engineers of Japan Vol.60-D, No.11, pp.990–997 (1977).Google Scholar
  4. [4]
    K. Morita, H. Umeo, and K. Sugata, Accepting Abilities of Offside-free Two-dimensional Marker Automata — The simulation of Four-way Automata by Three-way Tape-bounded Turing Machines, The Technical Reports of the Institute of Electronics and Communication Engineers of Japan Vol.AL79,No.19,pp.1–10(1979).Google Scholar
  5. [5]
    K. Inoue and A. Nakamura, Some Properties of Two-Dimensional On-Line Tessellation Acceptors, Information Sciences 13, pp.95–121 (1977).Google Scholar
  6. [6]
    K. Inoue and I. Takanami, A Note on Deterministic Three-Way Tape-Bounded Two-Dimensional Turing Machines, Information Sciences 20, pp.41–55 (1980).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • Akira Ito
    • 1
  • Katsushi Inoue
    • 2
  • Itsuo Takanami
    • 2
  1. 1.Technical CollegeYamaguchi UniversityUbeJapan
  2. 2.Faculty of EngineeringYamaguchi UniversityUbeJapan

Personalised recommendations