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 PC+...
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| Format: | Article |
| Language: | English |
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Hindawi Limited
2013-01-01
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| Series: | The Scientific World Journal |
| Online Access: | http://dx.doi.org/10.1155/2013/691439 |
| Summary: | 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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| ISSN: | 1537-744X |