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Relativised cellular automata and complexity classes

Extended abstract
  • Meena Mahajan
  • Kamala Krithivasan
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 560)

Abstract

Some of the fundamental problems concerning cellular automata (CA) are as follows:
  1. 1)

    Are linear-time CA (lCA) more powerful than real-time CA (rCA)?

     
  2. 2)

    Are nonlinear-time CA more powerful than linear-time CA?

     
  3. 3)

    Does one-way communication reduce the power of a CA?

     
These questions have been open for a long time. In this paper, we address these questions with respect to tally languages in relativised worlds, interpreting time-varying CA (TVCA) as oracle machines. We construct
  1. a)

    oracles which separate rCA from lCA and lCA from CA,

     
  2. b)

    oracle classes under which the CA classes coincide, and

     
  3. c)

    oracles which leave the CA classes unchanged.

     

Further, with rCA and lCA at the base, we build a hierarchy of relativised CA complexity classes between rCA and CA, and study the dependencies between the classes in this hierarchy.

Keywords

Cellular Automaton Turing Machine Cellular Automaton Transition Rule Input Word 
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.

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References

  1. Bo.
    R. V. Book, Tally languages and complexity classes, Inform. and Control 26 (1974) 186–193.CrossRefGoogle Scholar
  2. BC.
    W. Bucher and K. Culik II, On real-time and linear-time cellular automata, RAIRO Inform. Theor. 18(4) (1984) 307–325.Google Scholar
  3. CC.
    C. Choffrut and K. Culik II, On real-time cellular automata and trellis automata, Acta Inform. 21 (1984) 393–409.CrossRefGoogle Scholar
  4. CIV.
    J. Chang, O. Ibarra and A. Vergis, On the power of one-way communication, J. ACM 35(3) (1988) 697–726.CrossRefGoogle Scholar
  5. Dy.
    C. Dyer, One-way bounded cellular automata, Inform. and Control 44 (1980) 54–69.Google Scholar
  6. IJ1.
    O. Ibarra and T. Jiang, Relating the power of cellular arrays to their closure properties, Theor. Computer Science 57 (1988) 225–238.CrossRefGoogle Scholar
  7. IJ2.
    O. Ibarra and T. Jiang, On the computing power of one-way cellular arrays, SIAM J. Comput. 16 (1987) 46–55.Google Scholar
  8. IPK.
    O. Ibarra, M. Palis and S. Kim, Some results concerning linear iterative (systolic) arrays, J. Parallel and Distributed Comput. 2 (1985) 182–218.CrossRefGoogle Scholar
  9. Kos.
    S. Kosaraju, On some open problems in the theory of cellular automata, IEEE Trans. on Comput. C-23 (1974) 561–565.Google Scholar
  10. MK1.
    Meena Mahajan and Kamala Krithivasan, Some results on time-varying and relativised cellular automata, Technical Report Aug 90, Dept. of Computer Science, IIT Madras; submitted for publication.Google Scholar
  11. MK2.
    Meena Mahajan and Kamala Krithivasan, Relativised cellular automata and complexity classes, Technical Report Oct 90, Dept. of Computer Science, IIT Madras.Google Scholar
  12. Sm1.
    A. Smith III, Cellular automata complexity trade-offs, Inform. and Control 18 (1971) 466–482.CrossRefGoogle Scholar
  13. Sm2.
    A. Smith III, Real-time language recognition by one-dimensional cellular automata, J. Comput. System. Sci. 6 (1972 233–253.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Meena Mahajan
    • 1
  • Kamala Krithivasan
    • 1
  1. 1.Department of Computer Science & EngineeringIndian Institute Of TechnologyMadrasIndia

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