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Yasuo Uchida Takao Ito Makoto Sakamoto Kazuyuki Uchida Takashi Ide Ryoju Katamune Hiroshi Furutani Michio Kono Tsunehiro Yoshinaga 《Artificial Life and Robotics》2012,16(4):555-558
M. Blum and C. Hewitt first proposed two-dimensional automata as a computational model of two-dimensional pattern processing
in 1967, and investigated their pattern recognition abilities. Since then, many researchers in this field have investigated
many properties of automata on a two- or three-dimensional tape. However, the question of whether processing four-dimensional
digital patterns is much more difficult than processing two- or three-dimensional ones is of great interest from both theoretical
and practical standpoints. Thus, the study of four-dimensional automata as a computational model of four-dimensional pattern
processing has been meaningful. This article introduces a cooperating system of four-dimensional finite automata as one model
of four-dimensional automata. A cooperating system of four-dimensional finite automata consists of a finite number of four-dimensional
finite automata and a four-dimensional input tape, where these finite automata work independently (in parallel). The finite
automata whose input heads scan the same cell of the input tape can communicate with each other, i.e., every finite automaton
is allowed to know the internal states of other finite automata on the cell it is scanning at the moment. In this article
we mainly investigate the accepting powers of a cooperating system of seven-way four-dimensional finite automata. The seven-way
four-dimensional finite automaton is a four-dimensional finite automaton whose input head can move east, west, south, north,
up, down, or in the future, but not in the past, on a four-dimensional input tape. 相似文献
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Yasuo Uchida Takao Ito Makoto Sakamoto Takashi Ide Kazuyuki Uchida Ryuju Katamune Hiroshi Furutani Michio Kono Satoshi Ikeda Tsunehiro Yoshinaga 《Artificial Life and Robotics》2012,16(4):529-532
In 1967, M. Blum and C. Hewitt first proposed two-dimensional automata as a computational model of two-dimensional pattern
processing. Since then, many researchers in this field have been investigating the many properties of two- or three-dimensional
automata. In 1977, C.R. Dyer and A. Rosenfeld introduced an acceptor on a two-dimensional pattern (or tape) called the pyramid cellular acceptor, and demonstrated that many useful recognition tasks are executed by pyramid cellular acceptors in a time which is proportional
to the logarithm of the diameter of the input. They also introduced a bottom-up pyramid cellular acceptor, which is a restricted version of the pyramid cellular acceptor, and proposed some interesting open problems about bottom-up
pyramid cellular acceptors. On the other hand, we think that the study of four-dimensional automata has been meaningful as
the computational model of four-dimensional information processing such as computer animation, moving picture processing,
and so forth. In this article, we investigate bottom-up pyramid cellular acceptors with four-dimensional layers, and show
some of their accepting powers. 相似文献
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Yasuo Uchida Makoto Sakamoto Ayumi Taniue Ryuju Katamune Takao Ito Hiroshi Furutani Michio Kono 《Artificial Life and Robotics》2010,15(4):385-388
Informally, the parallel Turing machine (PTM) proposed by Wiedermann is a set of identical usual sequential Turing machines
(STMs) cooperating on two common tapes: a storage tape and an 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 7 years or
so, automata on a four-dimensional tape have been proposed as computational models of four-dimensional pattern processing,
and several properties of such automata have been obtained. We proposed a four-dimensional parallel Turing machine (4-PTM),
and dealt with a hardware-bounded 4-PTM in which each side-length of each input tape is equivalent. We believe that this machine
is useful in measuring the parallel computational complexity of three-dimensional images. In this work, we continued the study
of the 3-PTM, in which each side-length of each input tape is equivalent, and investigated some of its accepting powers. 相似文献
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