Trace Monoid - Examples

Examples

Consider the alphabet . A possible dependency relation is

\begin{matrix} D &=& \{a,b\}\times\{a,b\} \quad \cup \quad \{a,c\}\times\{a,c\} \\ &=& \{a,b\}^2 \cup \{a,c\}^2 \\ &=& \{ (a,b),(b,a),(a,c),(c,a),(a,a),(b,b),(c,c)\} \end{matrix}

The corresponding independency is

Therefore, the letters commute. Thus, for example, a trace equivalence class for the string would be

The equivalence class is an element of the trace monoid.

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