Computation theory of cellular automata

@article{Wolfram1984ComputationTO,
  title={Computation theory of cellular automata},
  author={S. Wolfram},
  journal={Communications in Mathematical Physics},
  year={1984},
  volume={96},
  pages={15-57}
}
  • S. Wolfram
  • Published 1984
  • Mathematics
  • Communications in Mathematical Physics
Self-organizing behaviour in cellular automata is discussed as a computational process. Formal language theory is used to extend dynamical systems theory descriptions 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. Many examples are given. The sizes of the minimal grammars for these languages provide measures of the complexities of the sets. This complexity is usually found to be… Expand
300 Citations
Global properties of cellular automata
  • 56
Inferring the Limit Behavior of Some Elementary Cellular Automata
  • 1
A complexity analysis of the elementary cellular automaton of rule 122
  • 19
  • Highly Influenced
On the Computational Complexity of Finite Cellular Automata
  • Klaus Sutner
  • Computer Science, Mathematics
  • J. Comput. Syst. Sci.
  • 1995
  • 76
Evolution complexity of the elementary cellular automaton of rule 22
  • 5
A brief history of cellular automata
  • 351
  • PDF
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 53 REFERENCES
Statistical mechanics of cellular automata
  • 2,549
  • PDF
Algebraic properties of cellular automata
  • 404
  • PDF
Universality and complexity in cellular automata
  • 1,903
  • PDF
Real-Time Language Recognition by One-Dimensional Cellular Automata
  • A. Smith
  • Computer Science
  • J. Comput. Syst. Sci.
  • 1972
  • 208
Two-dimensional cellular automata
  • 459
  • PDF
The Constructibility of a Configuration in a Cellular automaton
  • Takeo Yaku
  • Computer Science, Mathematics
  • J. Comput. Syst. Sci.
  • 1973
  • 31
Cellular automata as models of complexity
  • 1,300
  • PDF
Finite State Languages
  • 378
...
1
2
3
4
5
...