Titlebook: Associative Digital Network Theory; An Associative Algeb Nico F. Benschop Book Apr 2009Latest edition Springer Science+Business Media B.V.

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Lecture Notes in Computer Sciencech input and input-sequence maps the state set onto the same number of next states. CR-machines are analysed by their sequential closure (semigroup), which is shown to be a ., that is: a semi-direct product . |>(.×.) of a left- and a right-copy semigroup, and a group. So in general a CR-machine is a

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JSCL: A Middleware for Service Coordinationsic principles in theory and practice. State machines with isomorphic closures are defined equivalent. Each finite semigroup . can be represented by at most |.|+1 states, viz. itself, possibly extended by a left-identity. So state set . can be expanded to semigroup . to represent .. It is shown that

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Frédéric Mallet,Grygoriy Zholtkevych form a subgroup .. with |..|=|..|/.. The subgroup of order .−1, the . .. of .., extends Fermat’s Small Theorem (.) to mod .., consisting of .−1 residues with ..≡. mod ... The concept of ., e.g. .′ in . extension ..≡.′.+1 mod .., is crucial in expanding residue arithmetic to integers, and to allow a