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)


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.


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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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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