Transformation Semigroups and State Machines
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Date
2019
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Université de M'sila
Abstract
A transformation semigroup is a pair (Q; S) consisting of a finite set Q, a finie semigroup S and a semigroup action λ : Q X S⟶ Q, (q, s ⟼ s (q) which means :
(i) ∀q Q, ∀s, t S : st (q) = s (t (q)) ,
(ii) ∀s, t S,∀q Q, s (q) = t (q)⟹ s = t.
A state machine or a semiautomation is an ordered triple M = (Q, Σ, F ), where Q and are finite sets and F : Q X Σ⟶ Q is a partial function. In this paper, we give the construction of state machines associate a direct product, the cascade product and wreath product of transformations semigroups.
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Keywords
semigroup, semigroup action, morphism semigroup, transformation semi-group, state machine.