Abstract
Recently, due to the advances in many application areas such as computer animation, motion image processing, and so forth, it has become increasingly apparent that the study of four-dimensional pattern processing is of crucial importance. Thus, we think that research into four-dimensional automata as a computational model of four-dimensional pattern processing is also meaningful. This article introduces four-dimensional multicounter automata, and investigates some of their properties. We show the differences between the accepting powers of seven-way and eight-way four-dimensional multicounter automata, and between the accepting powers of deterministic and nondeterministic seven-way four-dimensional multicounter automata.
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References
K Inoue et al. (1979) ArticleTitleThree-way two-dimensional multicounter automata Inf Sci 19 1–20 Occurrence Handle0442.68038 Occurrence Handle10.1016/0020-0255(79)90029-X
A Szepietowski (1991) ArticleTitleOn three-way two-dimensional multicounter automata Inf Sci 55 35–47 Occurrence Handle0717.68072 Occurrence Handle1080447 Occurrence Handle10.1016/0020-0255(91)90004-E
Blum M, et al. (1967) Automata on a two-dimensional tape. IEEE Symposium of Switching and Automata Theory, pp 155–160
SA Greibach (1976) ArticleTitleRemarks on the complexity of nondeterministic counter languages Theor Comput Sci 1 269–288 Occurrence Handle0332.68039 Occurrence Handle411257 Occurrence Handle10.1016/0304-3975(76)90072-4
Sakamoto M, et al. (1999) Three-dimensional multicounter automata. Proceedings of the 6th International Workshops on Parallel Image Processing and Analysis, pp 267–280
K Inoue et al. (1991) ArticleTitleA survey of two-dimensional automata theory Inf Sci 55 99–121 Occurrence Handle0717.68071 Occurrence Handle10.1016/0020-0255(91)90008-I
Sakamoto M (1999) Three-dimensional alternating Turing machines. PhD Thesis, Yamaguchi University
M Sakamoto et al. (2004) ArticleTitleA note on four-dimensional finite automata WSEAS Trans Comput 5 1651–1656
J Hartmanis (1972) ArticleTitleOn non-determinancy in simple computing devices Acta Informatica 1 336–344 Occurrence Handle0229.68014 Occurrence Handle317582 Occurrence Handle10.1007/BF00289513
AK Chandra et al. (1981) ArticleTitleAlternation J ACM 28 114–133 Occurrence Handle0473.68043 Occurrence Handle10.1145/322234.322243
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This work was presented in part at the 10th International Symposium on Artificial Life and Robotics, Oita, Japan, February 4–6, 2005
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Saito, M., Sakamoto, M., Nakama, Y. et al. Some properties of four-dimensional multicounter automata. Artif Life Robotics 10, 166–170 (2006). https://doi.org/10.1007/s10015-005-0373-5
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DOI: https://doi.org/10.1007/s10015-005-0373-5