Abstract
A two-dimensional nondeterministic on-line tessellation acceptor (2-NOTA) is a special type of real-time two-dimensional nondeterministic cellular automaton in which data flows from the upper-left corner to the lower-right corner. A two-dimensional alternating finite automaton (2-AFA) is an alternating finite automaton with a two-dimensional rectangular input whose input head can move in all four directions on the input. In this paper, we show that 2-NOTA's and 2-AFA's are incomparable. This answers in the negative an open question in [IT89a]. Closure properties of the classes of languages (i.e., sets of two-dimensional patterns) accepted by two-way, three-way, and four-way two-dimensional alternating finite automata and two-dimensional alternating finite automata with only universal states are also obtained which answer several open questions in [IN88].
Research supported in part by NSF Grants CCR-8918409 and CCR90-96221.
Research supported in part by NSERC Operating Grant OGP 0046613 and a grant from SERB, McMaster University, Canada.
This is a preview of subscription content, log in via an institution.
Preview
Unable to display preview. Download preview PDF.
References
Blum, M. and C. Hewitt, Automata on a 2-dimensional tape, IEEE Symp. on Switching and Automata Theory, (1967), pp. 155–160.
Hopcroft, J.E. and J.D. Ullman, Some results on tape-bounded Turing machines, J. ACM 16-1, 1967, pp. 168–177.
Hromkovic, J., K. Inoue and I. Takanami, Lower bounds for language recognition on two-dimensional alternating multihead machines, J. of Computer and System Sciences 38, (1989), pp. 431–451.
Ibarra, O. and R. Melson, Some results concerning automata on two-dimensional tapes, Intern. J. Comp. Math. 4-A, (1974), pp. 269–279.
Inoue, K., and A. Nakamura, Some properties of two-dimensional on-line tessellation acceptors, Info. Sci., (1977), pp. 95–121.
Inoue, K., and A. Nakamura, Nonclosure properties of two-dimensional on-line tessellation acceptors and one-way parallel sequential array acceptors, IECE of Japan Trans. (E), Sept., 1977, pp. 475–476.
Inoue, K., I. Takanami and H. Taniguchi, Two-dimensional alternating Turing machines, Theoret. Comp. Sci. 27, (1983), pp. 61–83.
Inoue, K., A. Ito, I. Takanami and H. Taniguchi, A space hierarchy result on two-dimensional alternating Turing machines with only universal states, Info. Sci. 35, (1985), pp. 79–90.
Inoue, K. and I. Takanami, A survey of two-dimensional automata theory, IMYCS, (1988), pp. 21–35.
Ito, A., K. Inoue, I. Takanami and H. Taniguchi, Two-dimensional alternating Turing machines with only universal states, Info. and Control 55, (1982), pp. 193–221.
Ito, A., K. Inoue, I. Takanami and H. Taniguchi, A note on space complexity of nondeterministic two-dimensional Turing machines, IECE of Japan Trans. (E) (1983), pp. 508–509.
Ito, A., K. Inoue and I. Takanami, A note on three-way two-dimensional alternating Turing machines, Info. Sci. 45, (1988), pp. 1–22.
Ito, A., K. Inoue and I. Takanami, A relationship between one-dimensional bounded cellular acceptors and two-dimensional alternating finite automata, Informatik-Skripten 21, T. U. Braunschweig (1988), pp. 60–76.
Ito, A., K. Inoue and I. Takanami, Deterministic two-dimensional on-line tessellation acceptors are equivalent to two-way two-dimensional alternating finite automata through 180°-rotation, Theoret. Comp. Sci. 66, (1989), pp. 273–287.
Ito, A., K. Inoue and I. Takanami, Some closure properties of the class of sets accepted by three-way two-dimensional alternating finite automata, The Trans. of the IEICE E 72, No. 4, (1989), pp. 348–350.
Selkow, S., One-pass complexity of digital picture properties, J. ACM 19 (2), (1972), pp. 283–295.
Sipser M., Halting space-bounded computations, Symp. on Foundations of Comp. Sci., (1978), pp. 73–74.
Szepietowski, A., On three-way two-dimensional Turing machines, Info. Sci. 47, (1989), pp. 135–147.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1991 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Ibarra, O.H., Jiang, T., Wang, H. (1991). Some results concerning 2-D on-line tessellation acceptors and 2-D alternating finite automata. In: Tarlecki, A. (eds) Mathematical Foundations of Computer Science 1991. MFCS 1991. Lecture Notes in Computer Science, vol 520. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-54345-7_65
Download citation
DOI: https://doi.org/10.1007/3-540-54345-7_65
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-54345-9
Online ISBN: 978-3-540-47579-8
eBook Packages: Springer Book Archive