Transitive Closure

Let:

• $X$ be the set of elements
• $\mathcal{R}$ be the set of relations
• ${\mathcal{R}}^2$ be the set of relations which can be reached from two hops of relations in $\mathcal{R}$
  • For example, (a,c) is reached by going through (a,b) -> (b,c)
• ${\mathcal{R}}^{\ast }$ is the entire transitive closure over $\mathcal{R}$