On the syntactic monoids associated with a class of synchronized codes.
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 P C (+) . In particular, we prove that, for such a code C, either C = A or Syn(C (+)) is isomorphic to a special submonoid of 𝒯 (l) (I) × 𝒯 (r) (Λ), where 𝒯 (l) (I) and 𝒯 (r) (Λ) are the full transformation semigroups on the nonempty sets I and Λ, respectively.
School of Mathematics, Yunnan Normal University, Kunming, Yunnan 650500, China.
Shou-feng
SF
Wang
D000465:Algorithms; D003198:Computer Simulation; D016247:Information Storage and Retrieval / Q000379:methods*; D008962:Models, Theoretical; D012815:Signal Processing, Computer-Assisted