A Relationship between Marker and Inkdot for Four-Dimensional Automata

A multi-marker automaton is a finite automaton which keeps marks as pebbles in the finite control, and cannot rewrite any input symbols but can make marks on its input with the restriction that only a bounded number of these marks can exist at any given time. An improvement of picture recognizability of the finite automaton is the reason why the multi-marker automaton was introduced. On the other hand, a multi-inkdot automaton is a conventional automaton capable of dropping an inkdot on a given input tape for a landmark, but unable to further pick it up. Due to the advances in many application areas such as moving image processing, computer animation, and so on, it has become increasingly apparent that the study of four-dimensional pattern processing has been of crucial importance. Thus, we think that the study of four-dimensional automata as a computational model of four-dimensional pattern processing has also been meaningful. This paper deals with marker versus inkdot over four-dimensional input tapes, and investigates some properties. Keywords— finite automaton, four-dimension, inkdot, marker, recognizability

[1]  W. Marsden.  I and J , 2012 .

[2]  Makoto Sakamoto,et al.  Some accepting powers of three-dimensional parallel Turing machines , 2008, Artificial Life and Robotics.

[3]  Makoto Sakamoto,et al.  Remarks on the recognizability of topological components by three-dimensional automata , 2008, Artificial Life and Robotics.

[4]  Makoto Sakamoto,et al.  Recognizability of multi-inkdot finite automata on four-dimensional input tapes , 2008 .

[5]  Ito.  Some Accepting Powers of Three-Dimensional Synchronized Alternating Turing Machines , 2007 .

[6]  Makoto Sakamoto,et al.  Some properties of three-dimensional synchronized alternating turing machines , 2006 .

[7]  Eitan M. Gurari,et al.  (Semi)alternating stack automata , 2005, Mathematical systems theory.

[8]  T. Makino,et al.  Three-dimensional multi-inkdot automata , 2005 .

[9]  Susumu Katayama,et al.  A Space Lower-Bound Technique for Three-Dimensional Alternating Turing Machines , 2004 .

[10]  Yue Wang,et al.  A note on one-pebble two-dimensional Turing machines , 2003, Electron. Notes Discret. Math..

[11]  Kevin Barraclough,et al.  I and i , 2001, BMJ : British Medical Journal.

[12]  Makoto Sakamoto,et al.  A Relationship between the Accepting Powers of Three-Dimensional Finite Automata and Time-Bounded Bottom-Up Pyramid Cellular Acceptors with Three-Dimensional Layers , 1998 .

[13]  H. Damasio,et al.  IEEE Transactions on Pattern Analysis and Machine Intelligence: Special Issue on Perceptual Organization in Computer Vision , 1998 .

[14]  Makoto Sakamoto,et al.  Three-Dimensional Alternating Turing Machines with Only Universal States , 1996, Inf. Sci..

[15]  Katsushi Inoue,et al.  The Effect of Inkdots for Two-Dimensional Automata , 1995, Int. J. Pattern Recognit. Artif. Intell..

[16]  Holger Petersen.  Some Results Concerning Two-Dimensional Turing Machines and Finite Automata , 1995, FCT.

[17]  Andrzej Szepietowski.  Turing Machines with Sublogarithmic Space , 1994, Lecture Notes in Computer Science.

[18]  松野 浩嗣.  Multihead Automata and Alternation , 1994 .

[19]  Makoto Sakamoto,et al.  Three-Dimensionally Fully Space Constructible Functions , 1994 .

[20]  Makoto Sakamoto,et al.  Simulation of Three-Dimensional One-Marker Automata by Five-Way Turing Machines , 1994, Inf. Sci..

[21]  Makoto Sakamoto,et al.  A note on three-dimensional alternating Turing machines with space smaller than log m , 1993, Inf. Sci..

[22]  Katsushi Inoue,et al.  Constant Leaf-Size Hierarchy of Two-Dimensional Alternating Turing Machines , 1994, Int. J. Pattern Recognit. Artif. Intell..

[23]  Akira Nakamura.  Three-dimensional connected pictures are not recognizable by finite-state acceptors , 1992, Inf. Sci..

[24]  Anna Slobodová,et al.  On the Power of One-Way Synchronized Alternating Machines with Small Space , 1992, Int. J. Found. Comput. Sci..

[25]  Desh Ranjan,et al.  Space Bounded Computations: Review and New Separation Results , 1991, Theor. Comput. Sci..

[26]  Katsushi Inoue,et al.  Complexity of Acceptance Problems for Two-Dimensional Automata , 1989, A Perspective in Theoretical Computer Science.

[27]  Katsushi Inoue,et al.  A Survey of Two-Dimensional Automata Theory , 1988, IMYCS.

[28]  K. N. King,et al.  Alternating Multihead Finite Automata , 1988, Theor. Comput. Sci..

[29]  Katsushi Inoue,et al.  A note on three-way two-dimensional alternating Turing machines , 1988, Inf. Sci..

[30]  M. W. Shields.  An Introduction to Automata Theory , 1988 .

[31]  Akira Nakamura,et al.  Detection of interlocking components in three-dimensional digital pictures , 1986, Inf. Sci..

[32]  Juraj Hromkovic.  On the Power of Alternation in Automata Theory , 1985, J. Comput. Syst. Sci..

[33]  Akira Nakamura,et al.  On the Recognition of Properties of Three-Dimensional Pictures , 1985, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[34]  Parallel Turing machines , 1984 .

[35]  Katsushi Inoue,et al.  A Note on Multihead On-Line Turing Machines , 1983 .

[36]  Katsushi Inoue,et al.  Two-Dimensional Alternating Turing Machines with Only Universal States , 1982, Inf. Control..

[37]  Katsushi Inoue,et al.  Two-dimensional alternating Turing machines , 1982, STOC '82.

[38]  Katsushi Inoue,et al.  A note on three-dimensional finite automata , 1982, Inf. Sci..

[39]  Azriel Rosenfeld,et al.  Three-Dimensional Digital Topology , 1981, Inf. Control..

[40]  K. N. King.  Measures of parallelism in alternating computation trees (Extended Abstract) , 1981, STOC '81.

[41]  D. Morgenthaler.  Three-Dimensional Digital Topology: The Genus. , 1980 .

[42]  Ivan Hal Sudborough,et al.  Efficient algorithms for path system problems and applications to alternating and time-space complexity classes , 1980, 21st Annual Symposium on Foundations of Computer Science (sfcs 1980).

[43]  Walter L. Ruzzo,et al.  Tree-size bounded alternation(Extended Abstract) , 1979, J. Comput. Syst. Sci..

[44]  Katsushi Inoue,et al.  A note on deterministic three-way tape-bounded two-dimensional Turing machines , 1980, Inf. Sci..

[45]  Paul F. Dietz,et al.  Recognition of Topological Equivalence of Patterns by Array Automata , 1980, J. Comput. Syst. Sci..

[46]  Burkhard Monien.  Two-Way Multihead Automata Over a One-Letter Alphabet , 1980, RAIRO Theor. Informatics Appl..

[47]  Katsushi Inoue,et al.  Three-way tape-bounded two-dimensional turing machines , 1979, Inf. Sci..

[48]  Katsushi Inoue,et al.  A Note on Bottom-Up Pyramid Acceptors , 1979, Inf. Process. Lett..

[49]  Katsushi Inoue,et al.  Cyclic closure properties of automata on a two-dimensional tape , 1978, Inf. Sci..

[50]  M. Blum,et al.  On the capability of finite automata in 2 and 3 dimensional space , 1977, 18th Annual Symposium on Foundations of Computer Science (sfcs 1977).

[51]  Katsushi Inoue,et al.  Some properties of two-dimensional on-line tessellation acceptors , 1977, Inf. Sci..

[52]  Anupam N. Shah.  Pebble automata on arrays , 1974, Comput. Graph. Image Process..

[53]  Oscar H. Ibarra,et al.  Some results concerning automata on two-dimensional tapes , 1974 .

[54]  Azriel Rosenfeld,et al.  Parallel / Sequential Array Automata , 1973, Inf. Process. Lett..

[55]  W. Beyer.  RECOGNITION OF TOPOLOGICAL INVARIANTS BY ITERATIVE ARRAYS , 1969 .