Algebraic Theory of Automata Networks: A Introduction

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SIAM, Jan 1, 2005 - Mathematics - 258 pages
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Algebraic Theory of Automata Networks investigates automata networks as algebraic structures and develops their theory in line with other algebraic theories. Automata networks are investigated as products of automata, and the fundamental results in regard to automata networks are surveyed and extended, including the main decomposition theorems of Letichevsky, and of Krohn and Rhodes. The text summarizes the most important results of the past four decades regarding automata networks and presents many new results discovered since the last book on this subject was published. Several new methods and special techniques are discussed, including characterization of homomorphically complete classes of automata under the cascade product; products of automata with semi-Letichevsky criterion and without any Letichevsky criteria; automata with control words; primitive products and temporal products; network completeness for digraphs having all loop edges; complete finite automata network graphs with minimal number of edges; and emulation of automata networks by corresponding asynchronous ones.

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Directed Graphs Automata and Automata Networks
KrohnRhodes Theory and Complete Classes
Without Letichevskys Criterion
Letichevskys Criterion
Primitive Products and Temporal Products
Finite StateHomogeneous Automata Networks and Asynchronous

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About the author (2005)

Chrystopher L. Nehaniv is co-organizer of the Adaptive Systems Research Group at the University of Hertfordshsire, England.