On the Computational Complexity of Finite Cellular Automata

@article{Sutner1995OnTC,
  title={On the Computational Complexity of Finite Cellular Automata},
  author={Klaus Sutner},
  journal={J. Comput. Syst. Sci.},
  year={1995},
  volume={50},
  pages={87}
}
  • Klaus Sutner
  • Published 1 February 1995
  • Computer Science
  • J. Comput. Syst. Sci.
We study the computational complexity of several problems with the evolution of configurations on finite cellular automata. In many cases, the problems turn out to be complete in their respective classes. For example, the problem of deciding whether a configuration has a predecessor is shown to be NLOG-complete for one-dimensional cellular automata. The problem is NP-complete for all dimensions higher than one. Similarly, the question whether a target configuration occurs in the orbit of a… 

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References

SHOWING 1-10 OF 17 REFERENCES

Computation theory of cellular automata

The sets of configurations generated after a finite number of time steps of cellular automaton evolution are shown to form regular languages and it is suggested that such undecidability is common in these and other dynamical systems.

The Constructibility of a Configuration in a Cellular automaton

  • T. Yaku
  • Computer Science
    J. Comput. Syst. Sci.
  • 1973

Algebraic properties of cellular automata

Algebraic techniques are used to give an extensive analysis of the global properties of a class of finite cellular automata, and the complete structure of state transition diagrams is derived in terms of algebraic and number theoretical quantities.

On the predictability of coupled automata: an allegory about chaos

The authors show a sharp dichotomy between systems of identical automata with symmetric global control whose behavior is easy to predict and those whose behavior is hard to predict. The division

De Bruijn Graphs and Linear Cellular Automata

Every recursive configuration that has a predecessor on a linear CA already has a recursive pr edecessor, and it is shown that it is in genera l impossible to comput e such a predecessor effect ively.

Classifying the Computational Complexity of Problems

A branch of computational complexity theory is described which attempts to expose more structure within the decidable side of the boundary by placing upper bounds on the amounts of computational resources which are needed to solve the problem.

The monotone and planar circuit value problems are log space complete for P

It is shown that Ladner's simulation of Turing mac]hines by boolean circuits seems to require an "adequate" set of gates, such as AND and NOT, but the same simulation is possible with monotone circuits using AND and OR gates only.

Undecidability of CA Classification Schemes

It is shown that it is undecidable to which class a given cellula r automaton belongs, even when choosing only between the two simp lest classes.