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, &Gamma_I) of (S, &Gamma) such that:

1. h &isin I

2. x &isin I &rarr x &isin &Gamma^*h

3. I - {h} is cycle-free

4. if x &isin I - {h} , then &Gamma^-1x &sub I .

To construct an interval starting with node h :

1. initially, set I := {h}

2. repeat I := I &cup { x &isin &Gamma I | &Gamma^-1 x &sube I }
   until there are no more additions.

Members of &Gamma I - I must be the heads of other intervals.

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