Skip to main content
SpringerLink
Log in
Book cover

Models of Massive Parallelism pp 199–229Cite as

Some Inverse Problems

  • Chapter

  • 138 Accesses

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

Abstract

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.

One picture is worth a thousand words.

Old folk saying

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

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. R. Balzer: An 8-state minimal solution to the firing-squad synchronization problem. Inform, and Control 10(1967) 22–42

    Article  Google Scholar 

  2. M. Blum and C. Hewitt: Automata on a 2-dimensional tape. Proc. 6th IEEE Annual Symp. on Switching and Automata theory (now FOCS) (1967) 179–190

    Google Scholar 

  3. S.N. Cole: Real computation by n-dimensional iterative arrays. IEEE Trans, on Computers C-18 (1969) 349–365

    Article  Google Scholar 

  4. K. Culik: Variations on the firing squad problem and applications. Inf. Proc. Letters 30 (1989) 153–157

    Article  MathSciNet  MATH  Google Scholar 

  5. C. Dyer: One-way bounded cellular automata. Inf. and Control 44 (1980) 261–281

    Article  MathSciNet  MATH  Google Scholar 

  6. P.C. Fisher: Generation of primes by a one-dimensional iterative array. J. Assoc. Comput. Mach. 12 (1965) 388–394

    Article  MathSciNet  Google Scholar 

  7. M. Garzon: Cyclic Automata. Theoret. Computer Sci. 53 (1987) 307–317

    Article  MathSciNet  MATH  Google Scholar 

  8. M. Garzon: Cayley Automata Theoret. Computer Sci. A 108 (1993) 83–102

    MathSciNet  MATH  Google Scholar 

  9. 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. 160–178

    Google Scholar 

  10. M. Garzon, Y. Zalcstein: The complexity of Grigorchuk groups with application to cryptography. Theoret. Computer Sci. 88:1 (1991) 83–98

    Article  MathSciNet  MATH  Google Scholar 

  11. D. Giammarresi, A. Restivo: Recognizable picture languages. Int. J. of Pattern Recognition and Artif. Intel. 6:2/3 (1992)

    Google Scholar 

  12. R. Grigorchuk: Degrees of growth of finitely generated groups and the theory of invariant means. Math. USSR Izv. 25 (1985) 259–300

    Article  MATH  Google Scholar 

  13. M. Gromov: Groups of polynomial growth and expanding maps. Inst. Hautes Etudes Scientifiques Publ. Math. 53 (1981) 53–78

    MathSciNet  MATH  Google Scholar 

  14. 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, 1992

    Google Scholar 

  15. 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. 233–255

    Google Scholar 

  16. 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. 256–280

    Google Scholar 

  17. F.C. Hennie: Iterative arrays of logical circuits. MIT Press, Cambridge MA, 1961

    Google Scholar 

  18. K. Inoue, I. Takanami, A. Nakamura: A note on two-dimensional finite automata. Inf. Process. Lett. 7 (1978) 49–52

    Article  MathSciNet  MATH  Google Scholar 

  19. 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. 72–91

    Google Scholar 

  20. T. Jiang: The synchronization of nonuniform networks of finite automata. Proc. IEEE Symp. on Foundations of Computer Science FOCS 30 (1989) 376–381

    Google Scholar 

  21. K. Kobayashi: The firing squad synchronization problem for two-dimensional arrays. Inf. and Control 34 (1977) 177–197

    Article  MATH  Google Scholar 

  22. C.G. Langton: Computation at the edge of chaos: phase transitions and emergent computation. Physica D 42 (1990) 12–37

    Article  MathSciNet  Google Scholar 

  23. J. Lipton, Y. Zalcstein: Word problems solvable in logspace. J. Assoc. for Comput. Mach. 24 (1977) 522–526

    Article  MathSciNet  MATH  Google Scholar 

  24. J. Mazoyer: A six-state minimal time solution to the firing squad synchronization problem. Theoret. Comput. Sci. 50(1987) 183–238

    Article  MathSciNet  MATH  Google Scholar 

  25. 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, Prance

    Google Scholar 

  26. J. Mazoyer, V. Terrier: Signals in one dimensional cellular automata. Rapport de recherche, LIP École Normale Supérieure de Lyon, Prance, 1993

    Google Scholar 

  27. J. Milnor: Advanced Problem 3603, Amer. Math. Monthly 75 (1968) 685–686

    Article  MathSciNet  Google Scholar 

  28. M. Minsky: Finite and Infinite Machines. Prentice-Hall, Englewood Cliffs NJ, 1967

    MATH  Google Scholar 

  29. E. Moore: Sequential machines, selected papers. Addison-Wesley, Reading MA, 1964

    MATH  Google Scholar 

  30. F.R. Moore, G.G. Langdon: A generalized firing squad problem. Inf. And Control 12 (1968) 212–220

    Article  MATH  Google Scholar 

  31. 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) 353–376

    Article  Google Scholar 

  32. K. Morita, S. Ueno: Parallel generation and parsing of array languages using reversible cellular automata. Preprint

    Google Scholar 

  33. J. Mycielski, D. Niwinski: Cellular automata on trees, a models for parallel computation. Fund. Informaticae XV (1991) 139–144

    MathSciNet  Google Scholar 

  34. M. Nivat, A. Saudi, V.R. Dare: Parallel generation of finite images. Int. J. of Pattern Recognition and Artif. Intel. 3:3/4 (1989) 279–294

    Article  Google Scholar 

  35. Z. Roka: One-way cellular automata on Cayley graphs. Preprint. LIP, École Normale Supérieure de Lyon, 1993

    Google Scholar 

  36. A. Rosenfeld: Picture languages (formal models for picture recognition). Academic press NY, 1979

    Google Scholar 

  37. P. Rujàn, Cellular Automata and Statistical Mechanical models. J. Statistical Physics 49 (1987) 139–232

    Article  MATH  Google Scholar 

  38. M. Saoudi, K. Rangarajan, V.R. Dare: Finite images generated by GL- systems. Int. J. of Pattern Recognition and Artif. Intel. 3 (1989) 459–467

    Article  Google Scholar 

  39. S.M. Selkow: One-pass complexity of digital picture properties. J. Assoc. Comput. Mach, 19 (1972) 283–295

    Article  MATH  Google Scholar 

  40. H. Siegelman and E. Sontag: On the computational power of neural nets. Proc. 5th Comput. Learning Theory Conf. COLT (1992) 440–449

    Google Scholar 

  41. A.R. Smith III: Cellular automata and formal languages. Proc. 11th IEEE Symp. on Switching and Automata Theory (now FOCS) (1970) 216–224

    Google Scholar 

  42. 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) 144–152

    Google Scholar 

  43. A.R. Smith III: Cellular automata complexity tradeoffs. Inform, and Control 18 (1971) 466–482

    Article  MATH  Google Scholar 

  44. A.R. Smith III: Real-time language recognition by one-dimensional cellular automata. J. Assoc. Comput. Mach. 6 (1972) 233–253

    MATH  Google Scholar 

  45. J. Tits: Free subgroups in linear groups. J. of Algebra 20 (1972) 250–270

    Article  MathSciNet  MATH  Google Scholar 

  46. 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) 259–319

    Google Scholar 

  47. A. Waksman: An optimal solution to the firing squad synchronization problem. Information and Control 8(1966) 66–78

    Article  MathSciNet  Google Scholar 

  48. S. Wolfram: Theory and Applications of Cellular Automata. World Scientific, Singapore, 1986

    MATH  Google Scholar 

Download references

Authors
  1. Old folk
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 1991 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

folk, O. (1991). Some Inverse Problems. In: Models of Massive Parallelism. Texts in Theoretical Computer Science. An EATCS Series. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-77905-3_10

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-77905-3_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-77907-7

  • Online ISBN: 978-3-642-77905-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation