Intervals

An interval is a subgraph that basically corresponds to a program loop.

An interval I with initial node h is the maximal subgraph (I, Γ_I) of (S, Γ) such that:

1. h ∈ I

2. x ∈ I → x ∈ Γ^*h

3. I - {h} is cycle-free

4. if x ∈ I - {h} , then Γ^-1x ⊂ I .

To construct an interval starting with node h :

1. initially, set I := {h}

2. repeat I := I ∪ { x ∈ Γ I | Γ^-1 x ⊆ I }
   until there are no more additions.

Members of Γ I - I must be the heads of other intervals.