Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
Skip to main content
Springer Nature Link
Log in

A survey of two-dimensional automata theory

  • Chapter 2 Machines
  • Conference paper
  • First Online:
Machines, Languages, and Complexity (IMYCS 1988)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 381))

Included in the following conference series:

  • 200 Accesses

Abstract

The main purpose of this paper is to survey several properties of alternating, nondeterministic, and deterministic two-dimensional Turing machines (including two-dimensional finite automata and marker automata), and to briefly survey cellular types of two-dimensional automata.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. H. Antelmann, L. Budach and H.A. Rollik, On universal traps, EIK 15, 3 (1979), 123–131.

    Google Scholar 

  2. T.Beyer, Recognition of topological invariants by iterative arrays, Ph.D.Thesis, MIT, 1970.

    Google Scholar 

  3. M.Blum and C.Hewitt, Automata on a two-dimensional tape, IEEE Symposium on Switching and Automata Theory, 1967, 155–160.

    Google Scholar 

  4. M.Blum and D.Kozen, On the power of the compass, Proc. of the 19th Annual Symp. on Foundations of Computer Science, 1978

    Google Scholar 

  5. M.Blum and W.J.Sakoda, On the capability of finite automata in 2 and 3 dimensional space, Proc. of the 18th Annual Symp. on Foundations of Computer Science, 1977, 147–161.

    Google Scholar 

  6. W.Bucher and K.Culik II, On real time and linear time cellular automata, Research Report 115, Institute fur Informationsverarbeitung, Technical University of Graz, 1983.

    Google Scholar 

  7. L.Budach, Environments, labyrinths and Automata, Lecture Notes in Computer Science 56, Springer Verlag, 1977.

    Google Scholar 

  8. —, Automata and Labyrinths, Math. Nachr. 86 (1978), 195–282.

    Google Scholar 

  9. L. Budach and C. Meinel, Environments and automata I, EIK 18, 1/2 (1982), 13–40.

    Google Scholar 

  10. —, Environments and automata II, EIK 18, 3 (1982), 115–139.

    Google Scholar 

  11. A.K. Chandra, D.C. Kozen and L.J. Stockmeyer, Alternation, J.Assoc.Comput.Mach. 28, 1 (1981), 114–133.

    Google Scholar 

  12. C.Choffrut and K.Culik II, On real-time cellular automata and trellis automata, Research Report F114, Institute fur Informationsverarbeitung, Technical University of Graz, 1983.

    Google Scholar 

  13. P. Dietz and S.R. Kosaraju, Recognition of topological equivalence of patterns by array automata, JCSS 2 (1980), 111–116.

    Google Scholar 

  14. C.R. Dyer, One-way bounded cellular automata, Information and Control 44 (1980),261–281.

    Google Scholar 

  15. —, Relation of one-way parallel/sequential automata to 2-d finite automata, Information Sciences 23 (1981), 25–30.

    Google Scholar 

  16. C.R.Dyer and A.Rosenfeld, Cellular pyramids for image analysis, University of Maryland, Computer Science Center, TR-544, AFOSR-77-3271, 1977.

    Google Scholar 

  17. —, Parallel image processing by memory-augmented cellular automata, IEEE Trans. on Pattern Analysis and Machine Intelligence, PAMI-3, 1 (1981), 29–41.

    Google Scholar 

  18. —, Triangle cellular automata, Information and Control 48 (1981), 54–69.

    Google Scholar 

  19. E.M. Ehlers and S.H. Von Solms, A hierarchy of random context grammars and automata, Information Sciences 42 (1987), 1–29.

    Google Scholar 

  20. M.J.Fisher, Two characterizations of the context sensitive languages, IEEE Symp. on Switching and Automata Theory (1969), 149–156.

    Google Scholar 

  21. J. Hartmanis, The structural complexity column, Bulletin of the EATCS, 33 (October 1987), 26–39.

    Google Scholar 

  22. A. Hemmerling, Normed two-plane traps for finite systems of cooperating compass automata, EIK 23, 8/9 (1987),, 453–470.

    Google Scholar 

  23. F. Hoffmann, One pebble does not suffice to search plane labyrinths, Lecture Notes in Computer Science 117 (Fundamentals of Computation Theory), 1981, 433–444.

    Google Scholar 

  24. J.E. Hopcroft and J.D. Ullman, Some results on tape-bounded Turing machines, J.Assoc.Comput.Math. 19, 2 (1972), 283–295.

    Google Scholar 

  25. — Introduction to Automata Theory, Languages, and Computation, Addison-Wesley, Reading, Mass. 1979.

    Google Scholar 

  26. J.Hromkovic, K.Inoue and I.Takanami, Lower bounds for language recognition on two-dimensional alternating multihead machines, To appear in JCSS.

    Google Scholar 

  27. O.H. Ibarra and R.T. Melson, Some results concerning automata on two-dimensional tapes, Intern.J.Computer Math. 4-A (1974), 269–279.

    Google Scholar 

  28. N.Immerman, Nondeterministic space is closed under complement, submitted for publication.

    Google Scholar 

  29. K.Inoue, Investigations of two-dimensional on-line tessellation acceptors (in Japanese), Ph.D.Thesis, Nagoya University, 1977.

    Google Scholar 

  30. K.Inoue and A.Nakamura, Some notes on parallel sequential array acceptors (in Japanese), IECE of Japan Trans.(D), March 1975, 167–169.

    Google Scholar 

  31. —, On the relation between two-dimensional on-line tessellation acceptors and one-dimensional bounded cellular acceptors (in Japanese), IECE of Japan Trans.(D), September 1976, 613–620.

    Google Scholar 

  32. —, Some properties of one-way parallel sequential array acceptors and two-dimensional one-marker automata (in Japanese), IECE of Japan Trans.(D), September 1976, 682–683.

    Google Scholar 

  33. —, Some properties of parallel sequential array acceptors and two-dimensional two-marker automata (in Japanese), IECE of Japan Trans.(D), September 1976, 680–681.

    Google Scholar 

  34. —, Some properties of two-dimensional on-line tessellation acceptors (in Japanese), IECE of Japan Trans.(D), October 1976, 695–702.

    Google Scholar 

  35. —, Some properties of two-dimensional on-line tessellation acceptors, Information Sciences 13 (1977), 95–121.

    Google Scholar 

  36. —, Some properties of two-dimensional automata with a one-letter alphabet-Recognizability of functions by two-dimensional automata-(in Japanese), IECE of Japan Trans.(D), September 1977, 679–686.

    Google Scholar 

  37. —, Nonclosure properties of two-dimensional on-line tessellation acceptors and one-way parallel sequential array acceptors, IECE of Japan Trans. (E), September 1977, 475–476.

    Google Scholar 

  38. —, Some properties on two-dimensional nondeterministic finite automata and parallel sequential array acceptors (in Japanese), IECE of Japan Trans. (D), November 1977, 990–997.

    Google Scholar 

  39. —, Two-dimensional multipass on-line tessellation acceptors, Information and Control 41, 3 (June 1979), 305–323.

    Google Scholar 

  40. —, Two-dimensional finite automata and unacceptable functions, Intern.J.Computer Math. Section A, 7 (1979), 207–213.

    Google Scholar 

  41. K. Inoue and I. Takanami, A note on closure properties of the classes of sets accepted by tape-bounded two-dimensional Turing machines, Information Sciences 15, 1 (1978), 143–158.

    Google Scholar 

  42. —, Cyclic closure properties of automata on a two-dimensional tape, Information Sciences 15, 1 (1978), 229–242.

    Google Scholar 

  43. —, A note on bottom-up pyramid acceptors, Information Processing Letters 8, 1 (1979), 34–37.

    Google Scholar 

  44. —, Three-way tape-bounded two-dimensional Turing machines, Information Sciences 17, 3 (1979), 195–220.

    Google Scholar 

  45. —, Closure properties of three-way and four-way tape-bounded two-dimensional Turing machines, Information Sciences 18, 3 (1979), 247–265.

    Google Scholar 

  46. —, Three-way two-dimensional multicounter automata, Information Sciences 19, 1 (1979), 1–20.

    Google Scholar 

  47. —, Some properties of three-way two-dimensional multicounter automata over square tapes (in Japanese), IECE of Japan Trans. (D), October 1979, 673–680.

    Google Scholar 

  48. —, A note on deterministic three-way tape-bounded two-dimensional Turing machines, Information Sciences 20, 1 (1980), 41–55.

    Google Scholar 

  49. —, A note on decision problems for three-way two-dimensional finite automata, Information Processing Letters 10, 5 (July 1980), 245–248.

    Google Scholar 

  50. K.Inoue, I.Takanami and J.Hromkovic, A leaf-size hierarchy of two-dimensional alternating Turing machines, Discrete Algorithms and Complexity, Academic Press (1987), 389–404.

    Google Scholar 

  51. K. Inoue, I. Takanami and A. Nakamura, A note on two-dimensional finite automata, Information Processing Letters 7, 1 (1978), 49–52.

    Google Scholar 

  52. —, Nonclosure property of nondeterministic two-dimensional finite automata under cyclic closure, Information Sciences 22, 1 (1980), 45–50.

    Google Scholar 

  53. —, Connected pictures are not recognizable by deterministic two-dimensional on-line tessellation acceptors, Computer Vision, Graphics, and Image Processing 26 (1984), 126–129.

    Google Scholar 

  54. —, A note on time-bounded bottom-up pyramid cellular acceptors, To appear in Information Sciences.

    Google Scholar 

  55. K.Inoue, I.Takanami and H.Taniguchi, Three-way two-dimensional simple multihead finite automata-Hierarchical properties-(in Japanese), IECE of Japan Trans. (D), February 1979, 65–72.

    Google Scholar 

  56. —, Three-way two-dimensional simple multihead finite automata-Closure properties-(in Japanese), IECE of Japan Trans. (D), April 1979, 273–280.

    Google Scholar 

  57. —, The accepting powers of two-dimensional automata over square tapes (in Japanese), IECE of Japan Trans. (D), February 1980, 113–120.

    Google Scholar 

  58. —, Two-dimensional alternating Turing machines, Theoretical Computer Science 27 (1983), 61–83.

    Google Scholar 

  59. A. Ito, k. Inoue, I. Takanami and H. Taniguchi, Two-dimensional alternating Turing machines with only universal states, Information and Control 55, 1–3 (1982), 193–221.

    Google Scholar 

  60. —, A note on space complexity of nondeterministic two-dimensional Turing machines, IECE of Japan Trans. (E), August 1983, 508–509.

    Google Scholar 

  61. —, Hierarchy of the accepting power of cellular space based on the number of state changes (in Japanese), IECE of Japan Trans. (D), September 1985, 1553–1561.

    Google Scholar 

  62. —, Relationships of the accepting powers between cellular space with bounded number of state-changes and other automata (in Japanese), IECE of Japan Trans. (D), September 1985, 1562–1570.

    Google Scholar 

  63. —, State-change bounded rectangular array cellular space acceptors with three-neighbor (in Japanese), IEICE of Japan Trans. (D), December 1987, 2339–2347.

    Google Scholar 

  64. A. Ito, K. Inoue and I. Takanami, A note on three-way two-dimensional alternating Turing machines, Information Sciences 45, 1 (1988), 1–22.

    Google Scholar 

  65. —, Deterministic on-line tessellation acceptors are equivalent to two-way two-dimensional alternating finite automata through 180° rotations, to appear in Theoretical Computer Science.

    Google Scholar 

  66. —, A relationship between one-dimensional bounded cellular acceptors and two-dimensional alternating finite automata, manuscript (1987).

    Google Scholar 

  67. —, The simulation of two-dimensional one-marker automata by three-way two-dimensional Turing machines, to appear in the fifth International Meeting of Young Computer Scientists, November 14–18, 1988, Czechoslovakia.

    Google Scholar 

  68. —, Some closure properties of the class of sets accepted by three-way two-dimensional alternating finite automata, submitted for publication.

    Google Scholar 

  69. K.Iwama, ASPACE(o(loglog n)) is regular, Research Report, KSU/ICS, Institute of Computer Sciences, Kyoto Sangyo University, March 1986.

    Google Scholar 

  70. E.B. Kinber, Three-way automata on rectangular tapes over a one-letter alphabet, Information Sciences 35 (1985), 61–77.

    Google Scholar 

  71. S.R. Kosaraju, On some open problems in the theory of cellular automata, IEEE Trans. on Computers C-23, 6 (1974), 561–565.

    Google Scholar 

  72. —, Fast parallel processing array algorithms for some graph problems, Proc. of the 11th Annual ACM Symp. on Theory of Computing (1979), 231–236.

    Google Scholar 

  73. K. Krithivasan and R. Siromoney, Array automata and operations on array languages, Intern.J.Computer Math. 4-A (1974), 3–30.

    Google Scholar 

  74. R.E.Ladner, R.J.Lipton and L.J.Stockmeyer, Alternating pushdown automata, Proc. of the 19th IEEE Symp. on Foundations of Computer Science (1978), 92–106.

    Google Scholar 

  75. C. Meinel, The importance of plane labyrinths, EIK 18, 7/8 (1982), 419–422.

    Google Scholar 

  76. D.L. Milgram and A. Rosenfeld, Array automata and array grammars, IFIP Congress 71 (1971), Booklet Ta2, 166–173.

    Google Scholar 

  77. D.L. Milgram, A region crossing problem for array-bounded automata, Information and Control 31 (1976), 147–152.

    Google Scholar 

  78. K.Morita, Computational complexity in one-and two-dimensional tape automata, Ph.D. Thesis, Osaka University, 1978.

    Google Scholar 

  79. K.Morita and K.Sugata, Three-way horizontally context-sensitive array grammars (in Japanese), Technical Report No.AL80-66, IECE of Japan (1981).

    Google Scholar 

  80. K.Morita, H.Umeo and K.Sugata, Computational complexity of L(m,n) tape-bounded two-dimensional tape Turing machines (in Japanese), IECE of Japan Trans. (D), November 1977, 982–989.

    Google Scholar 

  81. —, Language recognition abilities of several two-dimensional tape automata and their relation to tape complexities (in Japanese), IECE of Japan Trans. (D), December 1977, 1077–1084.

    Google Scholar 

  82. K.Morita, H.Umeo, H.Ebi and K.Sugata, Lower bounds on tape complexity of two-dimensional tape Turing machines (in Japanese), IECE of Japan Trans. (D), 1978, 381–386.

    Google Scholar 

  83. K.Morita, H.Umeo and K.Sugata, Accepting capability of offside-free two-dimensional marker automata-the simulation of four-way automata by three-way tape-bounded Turing machines-(in Japanese), Technical Report No.AL79-2, IECE of Japan, 1979.

    Google Scholar 

  84. A. Nakamura and K. Aizawa, Acceptors for isometric parallel context-free array languages, Information Processing Letters 13, Nos4–5 (1981), 182–186.

    Google Scholar 

  85. A.Nakamura and C.R.Dyer, Bottom-up cellular pyramids for image analysis, Proc. of the 4th Int.Joint Conf.Pattern Recognition, 1978.

    Google Scholar 

  86. K.Nakazono, K.Morita and K.Sugata, Accepting ability of linear time nondeterministic bottom-up pyramid cellular automata (in japanese), IEICE of Trans. (D), February 1988, 458–461.

    Google Scholar 

  87. J. Pecht, T-recognition of T-languages, a new approach to describe and program the parallel pattern recognition capabilities of d-dimensional tessellation structures, Pattern Recognition 19, 4 (1986), 325–338.

    Google Scholar 

  88. A. Rosenfeld, Some notes on finite-state picture languages, Information and Control 31 (1976), 177–184.

    Google Scholar 

  89. —, Picture Languages (Formal Models for Picture Recognition), Academic Press, New York, 1977.

    Google Scholar 

  90. A. Rosenfeld and D.L. Milgram, Parallel/sequential array automata, Information Processing Letters 2 (1973), 43–46.

    Google Scholar 

  91. W.J. Savitch, Relationships between nondeterministic and deterministic tape complexities, JCSS 4 (1970), 177–192.

    Google Scholar 

  92. S. Seki, Real-time recognition of two-dimensional tapes by cellular automata, Information Sciences 19 (1979), 179–198.

    Google Scholar 

  93. S.M. Selkow, One-pass complexity of digital picture properties, J.Assoc.Comput.Math. 19(2) (1972), 283–295.

    Google Scholar 

  94. A.N. Shah, Pebble automata on arrays, Computer Graphics and Image Processing 3 (1974), 236–246.

    Google Scholar 

  95. —, Pushdown automata on arrays, Information Sciences 25 (1981), 175–193.

    Google Scholar 

  96. M. Sipser, Halting space-bounded computations (Note), Theoretical Computer Science 10 (1980), 335–338.

    Google Scholar 

  97. R. Siromoney, Array languages and Lindenmayer systems — a survey, in’ The Book of L’ (eds. G. Rozenberg and A. Salomaa), Springer-Verlag, Berlin, 1985.

    Google Scholar 

  98. —, Advances in array languages, Lecture Notes in Computer Science 291 (Graph-Grammars and Their Application to Computer Science), Ehrig et al. (Eds.), 1987, 549–563.

    Google Scholar 

  99. R. Siromoney and G. Siromoney, Extended controlled table L-arrays, Information and Control 35 (1977), 119–138.

    Google Scholar 

  100. A.R.Smith III, Two-dimensional formal languages and pattern recognition by cellular automata, Proc. of the 12th Switching and Automata Theory (1971), 144–152.

    Google Scholar 

  101. —, Real-time language recognition by one-dimensional cellular automata, JCSS 6 (1972), 233–253.

    Google Scholar 

  102. R.E.Stearns, J.Hartmanis and P.M.Lewis II,, Hierarchies of memory limited computations, IEEE Conf.Rec.on Switching Circuit Theory and Logical Design (1965),, 179–190.

    Google Scholar 

  103. R.Szelepcsenyi, The method of forcing for nondeterministic automata, submitted for publication.

    Google Scholar 

  104. A. Szepietowski, A finite 5-pebble automaton can search every maze, Information Processing Letters 15, 5 (December 1982), 199–204.

    Google Scholar 

  105. —, There are no fully space constructible functions between loglog n and log n, Information Processing Letters 24, 6 (April 1987), 361–362.

    Google Scholar 

  106. —, On three-way two-dimensional Turing machines, manuscript (1987).

    Google Scholar 

  107. H.Taniguchi, K.Inoue, I.Takanami and S.Seki, (k,1)-neighborhood template-type bounded cellular acceptors (in Japanese), IECE of Japan Trans. (D), March 1981, 244–251.

    Google Scholar 

  108. —, (k,1)-neighborhood template-type bounded cellular acceptors-refinements of hierarchical properties-(in Japanese), IECE of Japan Trans. (D), September 1983, 1062–1069.

    Google Scholar 

  109. —, Relationship between the accepting powers of (k,1)-neighborhood template-type 1-dimensional bounded cellular acceptors and other types of 2-dimensional automata (in Japanese), IECE of Japan Trans. (D), October 1985, 1711–1718.

    Google Scholar 

  110. —, Closure properties of (k,1)-neighborhood template-type 1-dimensional bounded cellular acceptors (in Japanese), IECE of Japan Trans. (D), March 1986, 279–290.

    Google Scholar 

  111. K.Taniguchi and T.Kasami, Some decision problems for two-dimensional nonwriting automata (in Japanese), IECE of Japan Trans. (C), 1971, 578–585.

    Google Scholar 

  112. M. Toda, K. Inoue and I. Takanami, Two-dimensional pattern matching by two-dimensional on-line tessellation acceptors, Theoretical Computer Science 24 (1983), 179–194.

    Google Scholar 

  113. H.Umeo, K.Morita and K.Sugata, Pattern recognition by automata on a two-dimensional tape, IECE of Japan Trans. (D), November 1976, 817–824.

    Google Scholar 

  114. R. Vollmar, On cellular automata with a finite number of state changes, Comput.Suppl. 3 (1981), 181–191.

    Google Scholar 

  115. P.S.P. Wang, Finite-turn repetitive checking automata and sequential/parallel matrix languages, IEEE Trans. on Computers C-30, 5 (May 1981), 366–370.

    Google Scholar 

  116. Y.Yamamoto, K.Morita and K.Sugata, Space complexity for recognizing connectedness in three-dimensional patterns, IECE of Japan Trans. (E), 1981, 778–785.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Electronics, Faculty of Engineering, Yamaguchi University, 755, Ube, Japan

    Katsushi Inoue & Itsuo Takanami

Authors
  1. Katsushi Inoue
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Itsuo Takanami
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

J. Dassow J. Kelemen

Rights and permissions

Reprints and permissions

Copyright information

© 1989 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Inoue, K., Takanami, I. (1989). A survey of two-dimensional automata theory. In: Dassow, J., Kelemen, J. (eds) Machines, Languages, and Complexity. IMYCS 1988. Lecture Notes in Computer Science, vol 381. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0015929

Download citation

  • DOI: https://doi.org/10.1007/BFb0015929

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-51516-6

  • Online ISBN: 978-3-540-48203-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation