Encyclopedia of Complexity and Systems Science

2009 Edition
| Editors: Robert A. Meyers (Editor-in-Chief)

Cellular Automata and Language Theory

  • Martin Kutrib
Reference work entry
DOI: https://doi.org/10.1007/978-0-387-30440-3_54

Definition of the Subject

One of the cornerstones in the theory of automata is the early result of John von Neumann, who solved the logical problem of nontrivial self‐reproduction. He employed a mathematical device which is a multitude of interconnected identical finite-state machines operating in parallel to form a larger machine. He showed that it is logically possible for such a nontrivial computing device to replicate itself ad infinitum [97]. Such devices are commonly called cellular automata (abbreviated, CA), and can be considered as homogeneously structured models for massively parallel computing systems. The global behavior of cellular automata is achieved by local interactions only. While the underlying rules are quite simple, the global behavior may be rather complex. In general, it is unpredictable.

The data supplied to CAs can be arranged as strings of symbols. Instances of problems to solve can be encoded as strings with a finite number of different symbols. Furthermore,...

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Primary Literature

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Books and Reviews

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Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  • Martin Kutrib
    • 1
  1. 1.Institut für InformatikUniversität GiessenGiessenGermany