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International Conference on Foundations of Software Technology and Theoretical Computer Science

FSTTCS 1991: Foundations of Software Technology and Theoretical Computer Science pp 172–185Cite as

Relativised cellular automata and complexity classes

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Part of the book series: Lecture Notes in Computer Science ((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.

This research was partially supported by a grant from the Department of Science and Technology, Government of India.

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References

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Author information

Authors and Affiliations

  1. Department of Computer Science & Engineering, Indian Institute Of Technology, 600 036, Madras, India

    Meena Mahajan & Kamala Krithivasan

Authors
  1. Meena Mahajan
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  2. Kamala Krithivasan
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Editor information

Somenath Biswas Kesav V. Nori

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© 1991 Springer-Verlag Berlin Heidelberg

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Mahajan, M., Krithivasan, K. (1991). Relativised cellular automata and complexity classes. In: Biswas, S., Nori, K.V. (eds) Foundations of Software Technology and Theoretical Computer Science. FSTTCS 1991. Lecture Notes in Computer Science, vol 560. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-54967-6_68

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  • DOI: https://doi.org/10.1007/3-540-54967-6_68

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-54967-3

  • Online ISBN: 978-3-540-46612-3

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