Some Inverse Problems

  • Old folk
Part of the Texts in Theoretical Computer Science. An EATCS Series book series (TTCS)


As explained in Chapter 2, conventional computing requires encoding of information into strings of symbols over a given alphabet. Classical computation thus deals with recognition and generation problems of formal languages consisting of words (strings of symbols). Classical computational theories originated in attempts to understand calculation as performed by humans. All the resultant models (Turing machines, Church’s A-calculus, Chomsky grammars, Markov algorithms, etc.) are based on the seemingly sequential nature of conscioushuman calculation. They are inherently sequential.


Cellular Automaton Word Problem Turing Machine Cayley Graph Local Rule 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [B]
    R. Balzer: An 8-state minimal solution to the firing-squad synchronization problem. Inform, and Control 10(1967) 22–42CrossRefGoogle Scholar
  2. [B-H]
    M. Blum and C. Hewitt: Automata on a 2-dimensional tape. Proc. 6th IEEE Annual Symp. on Switching and Automata theory (now FOCS) (1967) 179–190Google Scholar
  3. [C]
    S.N. Cole: Real computation by n-dimensional iterative arrays. IEEE Trans, on Computers C-18 (1969) 349–365CrossRefGoogle Scholar
  4. [Cu]
    K. Culik: Variations on the firing squad problem and applications. Inf. Proc. Letters 30 (1989) 153–157MathSciNetMATHCrossRefGoogle Scholar
  5. [D]
    C. Dyer: One-way bounded cellular automata. Inf. and Control 44 (1980) 261–281MathSciNetMATHCrossRefGoogle Scholar
  6. [F]
    P.C. Fisher: Generation of primes by a one-dimensional iterative array. J. Assoc. Comput. Mach. 12 (1965) 388–394MathSciNetCrossRefGoogle Scholar
  7. [Gal]
    M. Garzon: Cyclic Automata. Theoret. Computer Sci. 53 (1987) 307–317MathSciNetMATHCrossRefGoogle Scholar
  8. [Ga2]
    M. Garzon: Cayley Automata Theoret. Computer Sci. A 108 (1993) 83–102MathSciNetMATHGoogle Scholar
  9. [Ga3]
    M. Garzon: Graphical Words and Languages. In: Proc. Int. Conf. on Words, Languages and Combinatorics, Kyoto, 1990. M. Ito, ed., World Scientific Publishing, Singapore, pp. 160–178Google Scholar
  10. [G-Z]
    M. Garzon, Y. Zalcstein: The complexity of Grigorchuk groups with application to cryptography. Theoret. Computer Sci. 88:1 (1991) 83–98MathSciNetMATHCrossRefGoogle Scholar
  11. [G-R]
    D. Giammarresi, A. Restivo: Recognizable picture languages. Int. J. of Pattern Recognition and Artif. Intel. 6:2/3 (1992)Google Scholar
  12. [Gri]
    R. Grigorchuk: Degrees of growth of finitely generated groups and the theory of invariant means. Math. USSR Izv. 25 (1985) 259–300MATHCrossRefGoogle Scholar
  13. [Gro]
    M. Gromov: Groups of polynomial growth and expanding maps. Inst. Hautes Etudes Scientifiques Publ. Math. 53 (1981) 53–78MathSciNetMATHGoogle Scholar
  14. [Gutl]
    H. Gutowitz (editor): Cellular automata: theory and applications. Proc. 3rd. Int. Conf. Cellular Automata, Los Alamos, 1991. Physica D 45 (1990) 431–440. Also issued as a separate book by MIT Press, 1992Google Scholar
  15. [Gut5]
    H.A. Gutowitz: Statistical Properties of Cellular Automata in the Context of Learning and Recognition, Part I: Introduction. In: Learning and Recognition - A Modern Approach, K.H. Zhao, (ed.) World Scientific Publishing, Singapore (1989), pp. 233–255Google Scholar
  16. [Gut6]
    H.A. Gutowitz: Statistical Properties of Cellular Automata in the Context of Learning and Recognition, Part II: Inverting Local Structure Theory Equations to Find Cellular Automata With Specified Properties. In: Learning and Recognition - A Modern Approach, K.H. Zhao, (ed.) World Scientific Publishing, Singapore (1989), pp. 256–280Google Scholar
  17. [H]
    F.C. Hennie: Iterative arrays of logical circuits. MIT Press, Cambridge MA, 1961Google Scholar
  18. [I-T-N]
    K. Inoue, I. Takanami, A. Nakamura: A note on two-dimensional finite automata. Inf. Process. Lett. 7 (1978) 49–52MathSciNetMATHCrossRefGoogle Scholar
  19. [I-T]
    K. Inoue, I. Takanami: A survey of two-dimensional finite automata. In: Proc. 5th Int. Meeting of Young Computer Scientists, J. Dassow and J. Kelemen (eds.). Lecture Notes in Computer Science, Vol. 381. Springer-Verlag, Berlin, 1989, pp. 72–91Google Scholar
  20. [J]
    T. Jiang: The synchronization of nonuniform networks of finite automata. Proc. IEEE Symp. on Foundations of Computer Science FOCS 30 (1989) 376–381Google Scholar
  21. [K]
    K. Kobayashi: The firing squad synchronization problem for two-dimensional arrays. Inf. and Control 34 (1977) 177–197MATHCrossRefGoogle Scholar
  22. [L]
    C.G. Langton: Computation at the edge of chaos: phase transitions and emergent computation. Physica D 42 (1990) 12–37MathSciNetCrossRefGoogle Scholar
  23. [L-Z]
    J. Lipton, Y. Zalcstein: Word problems solvable in logspace. J. Assoc. for Comput. Mach. 24 (1977) 522–526MathSciNetMATHCrossRefGoogle Scholar
  24. [Mal]
    J. Mazoyer: A six-state minimal time solution to the firing squad synchronization problem. Theoret. Comput. Sci. 50(1987) 183–238MathSciNetMATHCrossRefGoogle Scholar
  25. [Ma2]
    J. Mazoyer: A minimal time solution to the firing squad synchronization problem with only one bit of information exchanged. Rapport de Recherche 89–03, LIP-Ecole Normale de Lyon, PranceGoogle Scholar
  26. [M-T]
    J. Mazoyer, V. Terrier: Signals in one dimensional cellular automata. Rapport de recherche, LIP École Normale Supérieure de Lyon, Prance, 1993Google Scholar
  27. [M]
    J. Milnor: Advanced Problem 3603, Amer. Math. Monthly 75 (1968) 685–686MathSciNetCrossRefGoogle Scholar
  28. [Mi]
    M. Minsky: Finite and Infinite Machines. Prentice-Hall, Englewood Cliffs NJ, 1967MATHGoogle Scholar
  29. [Moo]
    E. Moore: Sequential machines, selected papers. Addison-Wesley, Reading MA, 1964MATHGoogle Scholar
  30. [M-L]
    F.R. Moore, G.G. Langdon: A generalized firing squad problem. Inf. And Control 12 (1968) 212–220MATHCrossRefGoogle Scholar
  31. [Mol]
    K. Morita, Y. Yamamoto, K. Sugata: Two-dimensional three-way array grammars and their acceptors. Int. J. of Pattern Recognition and Artificial Intelligence. 3:3/4 (1989) 353–376CrossRefGoogle Scholar
  32. [M-U]
    K. Morita, S. Ueno: Parallel generation and parsing of array languages using reversible cellular automata. PreprintGoogle Scholar
  33. [M-N]
    J. Mycielski, D. Niwinski: Cellular automata on trees, a models for parallel computation. Fund. Informaticae XV (1991) 139–144MathSciNetGoogle Scholar
  34. [N-S-D]
    M. Nivat, A. Saudi, V.R. Dare: Parallel generation of finite images. Int. J. of Pattern Recognition and Artif. Intel. 3:3/4 (1989) 279–294CrossRefGoogle Scholar
  35. [Rok]
    Z. Roka: One-way cellular automata on Cayley graphs. Preprint. LIP, École Normale Supérieure de Lyon, 1993Google Scholar
  36. [Ros]
    A. Rosenfeld: Picture languages (formal models for picture recognition). Academic press NY, 1979Google Scholar
  37. [R]
    P. Rujàn, Cellular Automata and Statistical Mechanical models. J. Statistical Physics 49 (1987) 139–232MATHCrossRefGoogle Scholar
  38. [S-R-D]
    M. Saoudi, K. Rangarajan, V.R. Dare: Finite images generated by GL- systems. Int. J. of Pattern Recognition and Artif. Intel. 3 (1989) 459–467CrossRefGoogle Scholar
  39. [Se]
    S.M. Selkow: One-pass complexity of digital picture properties. J. Assoc. Comput. Mach, 19 (1972) 283–295MATHCrossRefGoogle Scholar
  40. [S-S]
    H. Siegelman and E. Sontag: On the computational power of neural nets. Proc. 5th Comput. Learning Theory Conf. COLT (1992) 440–449Google Scholar
  41. [Sml]
    A.R. Smith III: Cellular automata and formal languages. Proc. 11th IEEE Symp. on Switching and Automata Theory (now FOCS) (1970) 216–224Google Scholar
  42. [Sm2]
    A.R. Smith III: Two-dimensional formal languages and pattern recognition by cellular automata. Proc. 12th IEEE Annual Symp. on Switching and Automata Theory (now FOCS) (1971) 144–152Google Scholar
  43. [Sm3]
    A.R. Smith III: Cellular automata complexity tradeoffs. Inform, and Control 18 (1971) 466–482MATHCrossRefGoogle Scholar
  44. [Sm3]
    A.R. Smith III: Real-time language recognition by one-dimensional cellular automata. J. Assoc. Comput. Mach. 6 (1972) 233–253MATHGoogle Scholar
  45. [T]
    J. Tits: Free subgroups in linear groups. J. of Algebra 20 (1972) 250–270MathSciNetMATHCrossRefGoogle Scholar
  46. [Yal]
    Y. Yamamoto, K. Morita, K. Sugata: Context-sensitivity of two-dimensional regular array grammars. Int. J. of Pattern Recognition and Artificial Intelligence. 3:3/4 (1989) 259–319Google Scholar
  47. [Wa]
    A. Waksman: An optimal solution to the firing squad synchronization problem. Information and Control 8(1966) 66–78MathSciNetCrossRefGoogle Scholar
  48. [Wo1]
    S. Wolfram: Theory and Applications of Cellular Automata. World Scientific, Singapore, 1986MATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Old folk

There are no affiliations available

Personalised recommendations