Calculating Exact Transitive Closure for a Normalized Affine Integer Tuple Relation

Abstract: An approach to calculate the exact transitive closure of a parameterized and normalized affine integer tuple relation is presented. A relation is normalized when it describes graphs of the chain topology only. A procedure of the normalization is attached. The exact transitive closure calculation is based on resolving a system of recurrence equations being formed from the input and output tuples of a normalized relation. The approach permits for calculating an exact transitive closure for a relation when the constraints of this closure are represented by both affine and non-linear forms. Examples of calculating the exact transitive closure of normalized affine integer tuple relations are presented.