Browsing by Author "Ghadbane, Nacer"

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    On the Noetherian Properties of Reduction System of Words
    (Université de M'sila, 2018-12) Ghadbane, Nacer
    For any set of symbols, denotes the set of all words of symbols over , including the empty string . The set denotes the free monoid generated by under the operation of concatenation with the empty string serving as identity. Let R be a nite set. We de ne the binary relation )R as follows, where u; v 2 : u)R v if there exist x; y 2 and (l;m) 2 R with u = xly and v = xmy. The structure ;)R is a reduction system of words and the relation )R is the reduction relation. Let ;)R be a reduction system of words. The relation )R is Noetherian if there is no in nite sequence w0;w1; ::: 2 such that for all i 0;wi)R wi+1. In this paper, we study properties of reduction systems of words and give conditions under which a reduction system of word is Noetherian.
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    Transformation Semigroups and State Machines
    (Université de M'sila, 2019) Ghadbane, Nacer
    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.