On maximal synchronous codes.
The paper contains, as the main result, a construction of maximal synchronous codes. More precisely, it is proved that for a given synchronous code \(X\) with a synchronous pair \((x,y)\) the code \(X\cup V\), where \(V=(xyA^*\cap A^*xy)\setminus A^*xyX^*xyA^*\setminus A^*xyX^+\setminus X^+xyA^*\setminus X^*\), is a maximal synchronous code. Then the pair \((xy,xy)\) is the synchronizing pair for \(X\cup V\). The above construction preserves the rationality of \(X\). It is also proved that each maximal synchronous code is a maximal one. Some examples of another interesting properties are given.
scientific article; zbMATH DE number 2056476
scientific article