RComp: a Mathematica package for computing with recursive sequences
Journal of Symbolic Computation - Special issue on symbolic computation in combinatorics
Supporting Timing Analysis by Automatic Bounding of LoopIterations
Real-Time Systems - Special issue on worst-case execution-time analysis
POPL '77 Proceedings of the 4th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
The Mathematica Book
Array Data Dependence Testing with the Chains of Recurrences Algebra
IWIA '04 Proceedings of the Innovative Architecture for Future Generation High-Performance Processors and Systems
Science of Computer Programming - Special issue: Static analysis symposium (SAS 2003)
Automatic Derivation of Loop Bounds and Infeasible Paths for WCET Analysis Using Abstract Execution
RTSS '06 Proceedings of the 27th IEEE International Real-Time Systems Symposium
Automatic Inference of Upper Bounds for Recurrence Relations in Cost Analysis
SAS '08 Proceedings of the 15th international symposium on Static Analysis
Valigator: A Verification Tool with Bound and Invariant Generation
LPAR '08 Proceedings of the 15th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning
Control-flow refinement and progress invariants for bound analysis
Proceedings of the 2009 ACM SIGPLAN conference on Programming language design and implementation
"Carbon Credits" for Resource-Bounded Computations Using Amortised Analysis
FM '09 Proceedings of the 2nd World Congress on Formal Methods
User-definable resource bounds analysis for logic programs
ICLP'07 Proceedings of the 23rd international conference on Logic programming
Interprocedurally analyzing polynomial identities
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
r-TuBound: loop bounds for WCET analysis (tool paper)
LPAR'12 Proceedings of the 18th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
Symbolic loop bound computation for WCET analysis
PSI'11 Proceedings of the 8th international conference on Perspectives of System Informatics
ATVA'12 Proceedings of the 10th international conference on Automated Technology for Verification and Analysis
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We present ABC, a software tool for automatically computing symbolic upper bounds on the number of iterations of nested program loops. The system combines static analysis of programs with symbolic summation techniques to derive loop invariant relations between program variables. Iteration bounds are obtained from the inferred invariants, by replacing variables with bounds on their greatest values. We have successfully applied ABC to a large number of examples. The derived symbolic bounds express non-trivial polynomial relations over loop variables. We also report on results to automatically infer symbolic expressions over harmonic numbers as upper bounds on loop iteration counts.