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Algebraic Theory of Automata Networks - An Introduction (Hardcover, Illustrated Ed)
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Algebraic Theory of Automata Networks - An Introduction (Hardcover, Illustrated Ed)
Series: SIAM Monographs on Discrete Mathematics & Applications, v. 11
Expected to ship within 12 - 17 working days
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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, such as those of semigroups, groups,
rings, and fields. The authors also investigate automata networks
as products of automata, that is, as compositions of automata
obtained by cascading without feedback or with feedback of various
restricted types or, most generally, with the feedback dependencies
controlled by an arbitrary directed graph. This self-contained book
surveys and extends the fundamental results in regard to automata
networks, including the main decomposition theorems of Letichevsky,
of Krohn and Rhodes, and of others. It 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. It contains several new methods
and special techniques not discussed in other books, 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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