A complete code C over an alphabet A is called synchronized if there exist x, y ∈ C* such that xA*∩A*y⊆C*. In this paper we describe the syntactic monoid Syn(C +) of C + for a complete synchronized code C over A such that C +, the semigroup generated by C, is a single class of its syntactic congruence PC+. In particular, we prove that, for such a code C, either C = A or Syn(C+) is isomorphic to a special submonoid of 𝒯l(I) × 𝒯r(Λ), where 𝒯l(I) and 𝒯r(Λ) are the full transformation semigroups on the nonempty sets I and Λ, respectively.
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机译:如果存在x,y∈C *使得xA *∩A*y⊆C*,则字母A上的完整代码C称为同步。在本文中,我们描述了C + sup>上的完整同步代码C上C + sup>的句法半形词Syn(C + sup>), C生成的半群是其句法一致性 P em> C em> + sup>的单类。特别是,我们证明,对于这样的代码 C em>, C em> = A em>或Syn( C em> < sup> + sup>)与&#x1d4af; em> l em> sup>( I em> )×&#x1d4af; em> r em> sup>(Λ),其中&#x1d4af; em> l em> sup>( I em>)和&#x1d4af; em> r em> sup>(Λ)是非空集 I em>和Λ上的完全变换半群。
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