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The Scientific World Journal
Volume 2013 (2013), Article ID 691439, 5 pages
http://dx.doi.org/10.1155/2013/691439
Research Article

On the Syntactic Monoids Associated with a Class of Synchronized Codes

School of Mathematics, Yunnan Normal University, Kunming, Yunnan 650500, China

Received 2 October 2013; Accepted 5 December 2013

Academic Editors: A. Assi and G. Bosi

Copyright © 2013 Shou-feng Wang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A complete code over an alphabet is called synchronized if there exist such that . In this paper we describe the syntactic monoid of for a complete synchronized code over such that , the semigroup generated by , is a single class of its syntactic congruence . In particular, we prove that, for such a code , either or is isomorphic to a special submonoid of , where and are the full transformation semigroups on the nonempty sets and , respectively.