Skip to main content
SpringerLink
Log in

Decision Problems

  • Chapter
Models of Massive Parallelism

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

  • 143 Accesses

Abstract

One of the puzzling aspects about local rules of cellular automata is that despite their behavioral complexity, they are describable by finite tables that require only finitely many symbols and can be fed as input to a conventional computer. It is therefore natural to ask whether one could, at least in principle, write a program for a von Neumann computer that would answer questions, as some sort of pre-processing or short-cut, about the effect in the large of local rule inputs. For instance one may ask, is the global effect of the input local rule injective? Is it surjective? If reversible, what is the inverse that will undo the change caused by the rule? And so forth.

Article Note

She whom I love is hard to catch and conquer, Hard, but O the Glory of winning were she won!

George Meredith

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

Access this chapter

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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. V.Z. Aladyev: Mathematical theory of nonhomogeneous structures and their applications. Central Statistics Board, Alinn-Valgus, Estonia, 1980

    Google Scholar 

  2. A. Amoroso, Y.N. Patt: Decision properties for surjectivity and injectivity of parallel maps for tesselation structures. J. Comput. Syst. Science 6 (1972) 448–464

    Article  MathSciNet  MATH  Google Scholar 

  3. B. Andrasfai: Cellular Automata in Trees. In: Finite and Infinite Sets. Math. Soc. Janos Bolyai, Eger, Hungary, 1981

    Google Scholar 

  4. R. Berger: The undecidability of the domino problem. Memoirs of the American Mathematical Society, Providence RI, 1966

    Google Scholar 

  5. D.P. Bovet, P. Crescenzi: Introduction to the theory of complexity. Prentice-Hall, Hertfordshire, 1994

    Google Scholar 

  6. K. Culik II: On invertible cellular automata. Complex Systems 1:6 (1987) 1035–1044

    MathSciNet  MATH  Google Scholar 

  7. G. Chartrand, L. Lesniak: Graphs and digraphs, 2nd edition. Wadsworth and Brooks/Cole, Monterey CA, 1986

    MATH  Google Scholar 

  8. B. Durand: Undecidability of the surjectivity problem for 2D cellular automata: a simplified proof. In: Fundamentals of Computation Theory, Z. Esik (ed.). Lecture Notes in Computer Science, Vol. 710. Springer-Verlag, Berlin, 1993 Full version to appear in J. Comput. Sys. Sci.

    Google Scholar 

  9. B. Durand: Inversion of 2D cellular automata: some complexity results. The oret. Comput. Sci. 134:2 (1994) 387–401

    MathSciNet  MATH  Google Scholar 

  10. M. Garzon, M. Zhang: Classifying neural networks. In: Proc. IEEE Southeast Conf. New Orleans, (1990) II 571–576

    Google Scholar 

  11. M.R Garey and D.S. Johnson: Computers and intractabillity: A guide to the theory of NP-completeness. W.H. Freeman, San Francisco, 1978

    Google Scholar 

  12. F. Green: NP-complete problems in cellular automata. Complex Systems 1:3 (1987) 453–474

    MathSciNet  MATH  Google Scholar 

  13. T. Head: One-dimensional cellular automata: injectivity from ambiguity. Complex Systems 3 (1989) 343–348

    MathSciNet  MATH  Google Scholar 

  14. J.E. Hopcroft, J.F. Ullman: Introduction to automata theory, languages and computation. Addison-Wesley, Reading MA, 1979

    MATH  Google Scholar 

  15. J. Kari: Decision problems concerning cellular automata. Ph.D. Thesis, Department of Mathematics, University of Turku, Finland, 1990

    Google Scholar 

  16. D.E. Muller and P.E. Schupp: The theory of ends, pushdown automata, and second-order logic. Theoret. Comput. Sci. 37 (1985) 51–75

    Article  MathSciNet  MATH  Google Scholar 

  17. M. Nasu: Local maps inducing surjective global maps of one-dimensional tesselation automata. Math. Syst. Theory 11:4 (1978) 327–351

    MathSciNet  MATH  Google Scholar 

  18. P. Orponen: On the computational power of discrete Hopfield nets. Preprint, Dept. of Computer Science, University of Helskinki, 1993

    Google Scholar 

  19. C. Papadimitriou: Computational complexity. Addison-Wesley, Reading MA, 1994

    MATH  Google Scholar 

  20. A. Saoudi, D.E. Muller and P.E. Schupp: Recognizable infinite trees and their complexity. In: Foundations of Software technology and theoretical computer science (Bangalore, 1990). Lecture Notes in Computer Science, Vol. 472. Springer-Verlag, Berlin, 1990, pp. 91–103

    Google Scholar 

  21. T. Sato: Decidability of some problems of linear cellular automata over finite commutative rings. Inform. Process. Lett. 46 (1993) 151–155

    Article  MathSciNet  MATH  Google Scholar 

  22. K. Sutner: σ—automata on Graphs. Complex Systems 2:1(1988) 1–28

    MathSciNet  MATH  Google Scholar 

  23. K. Sutner: Additive automata on graphs. Complex Systems 2:6 (1988) 641–661

    MathSciNet  Google Scholar 

  24. K. Sutner: De Bruijn graphs and linear cellular automata. Complex Systems 5:1 (1991) 19–30

    MathSciNet  MATH  Google Scholar 

  25. K. Sutner: The complexity of finite cellular automata. Forthcoming

    Google Scholar 

  26. T. Toffoli: Computation and construction universality of reversible cellular automata. J. Comput. Syst. Sci. 15 (1977) 213–231

    Article  MathSciNet  MATH  Google Scholar 

  27. J. von Neumann: Theory of self-reproducing automata. University of Illinois Press, Chicago IL, 1966

    Google Scholar 

  28. S. Wolfram: Theory and applications of cellular automata. World Scientific, Singapore, 1986

    MATH  Google Scholar 

  29. T. Yaku: The constructibility of a configuration in a cellular automaton. J. Comput. Syst. Sci. 7 (1973) 481–496

    Article  MathSciNet  MATH  Google Scholar 

  30. T. Yaku: Surjectivity of nondeterministic parallel maps induced by nondeterministic cellular automata. J. Comput. Syst. Sci. 12 (1976) 1–5

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematical Sciences, The University of Memphis, Winfield Dunn Building, Room 373, 38152, Memphis, Tennessee, USA

    Prof. Dr. Max Garzon

Authors
  1. Prof. Dr. Max Garzon
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 1995 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Garzon, M. (1995). Decision 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_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-77905-3_5

  • 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