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 (n 2), 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.
References
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).
A.Rosenfeld, Picture Languages — Formal models for Picture Recognition, Academic Press (1979).
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).
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).
K. Inoue and A. Nakamura, Some Properties of Two-Dimensional On-Line Tessellation Acceptors, Information Sciences 13, pp.95–121 (1977).
K. Inoue and I. Takanami, A Note on Deterministic Three-Way Tape-Bounded Two-Dimensional Turing Machines, Information Sciences 20, pp.41–55 (1980).
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1989 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Ito, A., Inoue, K., Takanami, I. (1989). The simulation of two-dimensional one-marker automata by three-way turing machines. In: Dassow, J., Kelemen, J. (eds) Machines, Languages, and Complexity. IMYCS 1988. Lecture Notes in Computer Science, vol 381. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0015930
Download citation
DOI: https://doi.org/10.1007/BFb0015930
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-51516-6
Online ISBN: 978-3-540-48203-1
eBook Packages: Springer Book Archive