A heuristic for deriving loop functions
IEEE Transactions on Software Engineering
An analysis of loop latency in dataflow execution
ISCA '92 Proceedings of the 19th annual international symposium on Computer architecture
A Knowledge-Based Approach to the Analysis of Loops
IEEE Transactions on Software Engineering
Supporting Timing Analysis by Automatic Bounding of LoopIterations
Real-Time Systems - Special issue on worst-case execution-time analysis
Communications of the ACM
The new math of computer programming
Communications of the ACM
An axiomatic basis for computer programming
Communications of the ACM
IEEE Transactions on Software Engineering
Deriving Annotations for Tight Calculation of Execution Time
Euro-Par '97 Proceedings of the Third International Euro-Par Conference on Parallel Processing
Finding Invariant assertions for proving programs
Proceedings of the international conference on Reliable software
Bounding Loop Iterations for Timing Analysis
RTAS '98 Proceedings of the Fourth IEEE Real-Time Technology and Applications Symposium
A hybrid approach for resource-based comparison of adaptable Java applications
Science of Computer Programming
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This paper addresses the problem of loop iteration number estimation, applied to linear loops. This is important to statically put an upper bound on the execution time of real-time systems and implement timing constraint verification. In our approach, matrix calculation is applied to derive the analytical equation that holds the number of iterations as a solution, and it is proved that such solution is related to a zero of an exponential function of the eigenvalues. So, the number of iterations turns out to be an implicit variable of the equation, which can be easily exactly calculated for loops depending on few free variables.