On the Equivalence of Two Systems of Affine Recurrence EquationsReport as inadecuate




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1 A3 - Advanced analysis to code optimization UP11 - Université Paris-Sud - Paris 11, Inria Saclay - Ile de France

Abstract : This paper deals with the problem of deciding whether two Systems of Affine Recurrence Equations are equivalent or not. A solution to this problem would be a first step toward algorithm recognition, an important tool in program analysis, optimization and parallelization. We first prove that in the general case, the problem is undecidable. The proof is by reducing any instance of Hilbert-s tenth problem the solution of Diophantine equations to the equivalence of two SAREs. We then show that there neverthele- ss exists a semi-algorithm, in which the key ingredient is the computation of transitive closures of affine relations. This is again an undecidable problem which has been extensively studied. Many partial solutions are known. We then report on a pilot implementation of the algorithm, describe its limitations, and point to unsolved problems.

Keywords : PROGRAM OPTIMIZATION PROGRAM ANALYSIS SYSTEM OF AFFINE RECURRENCE EQUATIONS PROGRAM EQUIVALENCE





Author: Denis Barthou - Paul Feautrier Xavier Redon

Source: https://hal.archives-ouvertes.fr/



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