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Semantical interprocedural parallelization: an overview of the PIPS project
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The Omega Library interface guide
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Translation validation for an optimizing compiler
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ACM Transactions on Embedded Computing Systems (TECS)
Uniformization of Affine Dependance Programs for Parallel Embedded System Design
ICPP '02 Proceedings of the 2001 International Conference on Parallel Processing
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PLILP '92 Proceedings of the 4th International Symposium on Programming Language Implementation and Logic Programming
On the Equivalence of Two Systems of Affine Recurrence Equations (Research Note)
Euro-Par '02 Proceedings of the 8th International Euro-Par Conference on Parallel Processing
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Theoretical Computer Science - Implementation and application of automata
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Formal Methods in System Design
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ACST'07 Proceedings of the third conference on IASTED International Conference: Advances in Computer Science and Technology
Inference rules for proving the equivalence of recursive procedures
Acta Informatica
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Proceedings of the 2009 ACM SIGPLAN conference on Programming language design and implementation
Equivalence Checking of Static Affine Programs Using Widening to Handle Recurrences
CAV '09 Proceedings of the 21st International Conference on Computer Aided Verification
Proceedings of the 46th Annual Design Automation Conference
CAV'07 Proceedings of the 19th international conference on Computer aided verification
Experience with Widening Based Equivalence Checking in Realistic Multimedia Systems
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isl: an integer set library for the polyhedral model
ICMS'10 Proceedings of the Third international congress conference on Mathematical software
Transitive closures of affine integer tuple relations and their overapproximations
SAS'11 Proceedings of the 18th international conference on Static analysis
Verification of source code transformations by program equivalence checking
CC'05 Proceedings of the 14th international conference on Compiler Construction
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Designers often apply manual or semi-automatic loop and data transformations on array- and loop-intensive programs to improve performance. It is crucial that such transformations preserve the functionality of the program. This article presents an automatic method for constructing equivalence proofs for the class of static affine programs. The equivalence checking is performed on a dependence graph abstraction and uses a new approach based on widening to find the proper induction hypotheses for reasoning about recurrences. Unlike transitive-closure-based approaches, this widening approach can also handle nonuniform recurrences. The implementation is publicly available and is the first of its kind to fully support commutative operations.