Abstract
Informally, the parallel Turing machine (PTM) proposed by Wiedermann is a set of identical usual sequential Turing machines (STMs) cooperating on two common tapes: storage tape and input tape. Moreover, STMs which represent the individual processors of a parallel computer can multiply themselves in the course of computation. On the other hand, during the past 25 years or so, automata on a three-dimensional tape have been proposed as computational models of three-dimensional pattern processing, and several properties of such automata have been obtained. We proposed a three-dimensional parallel Turing machine (3-PTM), and dealt with a hardware-bounded 3-PTM whose inputs are restricted to cubic ones. We believe that this machine is useful in measuring the parallel computational complexity of three-dimensional images. In this article, we continue the study of 3-PTM, whose inputs are restricted to cubic ones, and investigate some of its accepting powers.
Similar content being viewed by others
References
Rosenfeld A (1979) Picture languages. Academic Press, New York
Ito T, Sakamoto M, Nagamizu Y, et al (2007) Three-dimensional parallel Turing machines. In: Proceedings of the 12th International Symposium on Artificial Life and Robotics, Oita, Japan, pp 131–134
Sakamoto M (1999) Three-dimensional alternating Turing machines. PhD thesis, Yamaguchi University
Sakamoto M, Ito T, Tomozoe N, et al (2007) A survey of three-dimensonal automata. Papers of the Technical Meeting on Information Systems, IEE, Japan, IS-07-12, pp 11–17
Okinaka K, Inoue K, Ito A, et al (2002) A note on hardware-bounded parallel Turing machines. In: Proceedings of the 2nd International Conference on Information, Beijing, China, pp 90–100
Wiedermann J (1984) Parallel Turing machines. Technical Report RUU-CS-84-11, Department of Computer Science, University of Utrecht, The Netherlands
Author information
Authors and Affiliations
Corresponding author
Additional information
This work was presented in part at the 12th International Symposium on Artificial Life and Robotics, Oita, Japan, January 25–27, 2007
About this article
Cite this article
Ito, T., Sakamoto, M., Furutani, H. et al. Three-dimensional parallel Turing machines. Artif Life Robotics 13, 364–367 (2008). https://doi.org/10.1007/s10015-008-0500-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10015-008-0500-1