On the Syntactic Monoids Associated with a Class of Synchronized Codes

Abstract EN

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 ?l(I)×?r(Λ), where ?l(I) and ?r(Λ) are the full transformation semigroups on the nonempty sets I and Λ, respectively.