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On the Equivalence of Two Systems of Affine Recurrence Equations

Denis Barthou, +2 more
- pp 309-313
TLDR
In this paper, it was shown that the problem of deciding whether two Systems of Affine Recurrence Equations are equivalent or not is undecidable, but there is a semi-decision procedure, in which the key ingredient is the computation of transitive closures of affine relations.
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 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. We then show that there nevertheless exists a semi-decision procedure, in which the key ingredient is the computation of transitive closures of affine relations. This is a non-effective process 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.

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https://hal.inria.fr/inria-00072302
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On the Equivalence of Two Systems of Ane
Recurrence Equations
Denis Barthou, Paul Feautrier, Xavier Redon
To cite this version:
Denis Barthou, Paul Feautrier, Xavier Redon. On the Equivalence of Two Systems of Ane Recurrence
Equations. RR-4285, INRIA. 2001. �inria-00072302�
ISSN 0249-6399 ISRN INRIA/RR--4285--FR+ENG
apport
de recherche
THÈME 1
INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE
On the Equivalence of Two Systems of Affine
Recurrence Equations
Denis Barthou — Paul Feautrier — Xavier Redon
N° 4285
Octobre 2001
Unité de recherche INRIA Rocquencourt
Domaine de Voluceau, Rocquencourt, BP 105, 78153 Le Chesnay Cedex (France)
Téléphone : +33 1 39 63 55 11 — Télécopie : +33 1 39 63 53 30
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