The ALPHA language and its use for the design of systolic arrays
Journal of VLSI Signal Processing Systems - Special issue: algorithms and parallel VSLI architecture
Transitive closure of infinite graphs and its applications
International Journal of Parallel Programming - Special issue: selected papers from the eighth international workshop on languages and compilers for parallel computing
Automatic algorithm recognition and replacement: a new approach to program optimization
Automatic algorithm recognition and replacement: a new approach to program optimization
Scheduling and Automatic Parallelization
Scheduling and Automatic Parallelization
The Loop Parallelizer LooPo-Announcement
LCPC '96 Proceedings of the 9th International Workshop on Languages and Compilers for Parallel Computing
Symbolic Verification with Periodic Sets
CAV '94 Proceedings of the 6th International Conference on Computer Aided Verification
Proceedings of the conference on Design, Automation and Test in Europe - Volume 2
Automatic functional verification of memory oriented global source code transformations
HLDVT '03 Proceedings of the Eighth IEEE International Workshop on High-Level Design Validation and Test Workshop
Solving difference equations whose coefficients are not transcendental
Theoretical Computer Science
Distributed Implementation of OpenMP Based on Checkpointing Aided Parallel Execution
IWOMP '07 Proceedings of the 3rd international workshop on OpenMP: A Practical Programming Model for the Multi-Core Era
Computing the Transitive Closure of a Union of Affine Integer Tuple Relations
COCOA '09 Proceedings of the 3rd International Conference on Combinatorial Optimization and Applications
Equivalence Checking of Static Affine Programs Using Widening to Handle Recurrences
CAV '09 Proceedings of the 21st International Conference on Computer Aided Verification
Experience with Widening Based Equivalence Checking in Realistic Multimedia Systems
Journal of Electronic Testing: Theory and Applications
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
On domain-specific languages reengineering
GPCE'05 Proceedings of the 4th international conference on Generative Programming and Component Engineering
Equivalence checking of static affine programs using widening to handle recurrences
ACM Transactions on Programming Languages and Systems (TOPLAS)
Toward a distributed implementation of openMP using CAPE
PaCT'07 Proceedings of the 9th international conference on Parallel Computing Technologies
Checkpointing aided parallel execution model and analysis
HPCC'07 Proceedings of the Third international conference on High Performance Computing and Communications
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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.