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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| Language: | English |
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Wiley
2013-01-01
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| Series: | The Scientific World Journal |
| Online Access: | http://dx.doi.org/10.1155/2013/691439 |
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| author | Shou-feng Wang |
| author_facet | Shou-feng Wang |
| author_sort | Shou-feng Wang |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-5ff1cf973b2e41699b0609cae4711f1e |
| institution | OA Journals |
| issn | 1537-744X |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | The Scientific World Journal |
| spelling | doaj-art-5ff1cf973b2e41699b0609cae4711f1e2025-08-20T02:35:16ZengWileyThe Scientific World Journal1537-744X2013-01-01201310.1155/2013/691439691439On the Syntactic Monoids Associated with a Class of Synchronized CodesShou-feng Wang0School of Mathematics, Yunnan Normal University, Kunming, Yunnan 650500, ChinaA 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.http://dx.doi.org/10.1155/2013/691439 |
| spellingShingle | Shou-feng Wang On the Syntactic Monoids Associated with a Class of Synchronized Codes The Scientific World Journal |
| title | On the Syntactic Monoids Associated with a Class of Synchronized Codes |
| title_full | On the Syntactic Monoids Associated with a Class of Synchronized Codes |
| title_fullStr | On the Syntactic Monoids Associated with a Class of Synchronized Codes |
| title_full_unstemmed | On the Syntactic Monoids Associated with a Class of Synchronized Codes |
| title_short | On the Syntactic Monoids Associated with a Class of Synchronized Codes |
| title_sort | on the syntactic monoids associated with a class of synchronized codes |
| url | http://dx.doi.org/10.1155/2013/691439 |
| work_keys_str_mv | AT shoufengwang onthesyntacticmonoidsassociatedwithaclassofsynchronizedcodes |