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.

Read more about this topic:  Trace Monoid

Famous quotes containing the word examples:

    “No rules exist, and examples are simply life-savers answering the appeals of rules making vain attempts to exist.”
    —André Breton (1896–1966)

    “In the examples that I here bring in of what I have [read], heard, done or said, I have refrained from daring to alter even the smallest and most indifferent circumstances. My conscience falsifies not an iota; for my knowledge I cannot answer.”
    —Michel de Montaigne (1533–1592)