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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, ΓI) 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.