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Evolving Cellular Automata

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Book cover Computational Complexity

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Article Outline

Glossary

Definition of the Subject

Introduction

Cellular Automata

Computation in CAs

Evolving Cellular Automata with Genetic Algorithms

Previous Work on Evolving CAs

Coevolution

Other Applications

Future Directions

Acknowledgments

Bibliography

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Abbreviations

Cellular automaton (CA) :

Discrete‐space and discrete‐time spatially extended lattice of cells connected in a regular pattern.Each cell stores its state and a state‐transition function. At each time step, each cell applies the transition function to update its state based on its local neighborhood of cell states. The update of the system is performed in synchronous steps – i. e., all cells update simultaneously.

Cellular programming :

A variation of genetic algorithms designed to simultaneously evolve state transition rules and local neighborhood connection topologies for non‐homogeneous cellular automata.

Coevolution :

An extension to the genetic algorithm in which candidate solutions and their “environment” (typically test cases) are evolved simultaneously.

Density classification :

A computational task for binary CAs: the desired behavior for the CA is to iterate to an all-1s configuration if the initial configuration has a majority of cells in state 1, and to an all-0s configuration otherwise.

Genetic algorithm (GA) :

A stochastic search method inspired by the Darwinian model of evolution. A population of candidate solutions is evolved by reproduction with variation, followed by selection, for a number of generations.

Genetic programming :

A variation of genetic algorithms that evolves genetic trees.

Genetic tree :

Tree-like representation of a transition function, used by genetic programming algorithm.

Lookup table (LUT) :

Fixed‐length table representation of a transition function .

Neighborhood :

Pattern of connectivity specifying to which other cells each cell is connected.

Non‐homogeneous cellular automaton :

A CA in which each cell can have its own distinct transition function and local neighborhood connection pattern.

Ordering :

A computational task for one‐dimensional binary CAs with fixed boundaries: The desired behavior is for the CA to iterate to a final configuration in which all initial 0 states migrate to the left-hand side of the lattice and all initial 1 states migrate to the right-hand side of the lattice.

Particle :

Periodic, temporally coherent boundary between two regular domains in a set of successive CA configurations. Particles can be interpreted as carrying information about the neighboring domains. Collisions between particles can be interpreted as the processing of information, with the resulting information carried by new particles formed by the collision.

Regular domain :

Region defined by a set of successive CA configurations that can be described by a simple regular language.

Synchronization :

A computational task for binary CAs: the desired behavior for the CA is to iterate to a temporal oscillation between two configurations: all cells have state 1 and all cells have state 0s.

Transition function :

Maps a local neighborhood of cell states to an update state for the center cell of that neighborhood.

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Acknowledgments

This work has been funded by the Center on Functional Engineered Nano Architectonics (FENA), through the Focus Center Research Program of the Semiconductor Industry Association.

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Authors and Affiliations

  1. Computer Science Department, Portland State University, Portland, USA

    Martin Cenek & Melanie Mitchell

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  1. Martin Cenek
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  1. RAMTECH LIMITED, 122 Escalle Lane, Larkspur, CA, 94939, USA

    Robert A. Meyers Ph. D. (Editor-in-Chief) (Editor-in-Chief)

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Cenek, M., Mitchell, M. (2012). Evolving Cellular Automata. In: Meyers, R. (eds) Computational Complexity. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-1800-9_65

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