Interval analysis of microcontroller code using abstract interpretation of hardware and software
Proceedings of the 13th International Workshop on Software & Compilers for Embedded Systems
Static Analysis by Abstract Interpretation: A Mathematical Programming Approach
Electronic Notes in Theoretical Computer Science (ENTCS)
Solving systems of rational equations through strategy iteration
ACM Transactions on Programming Languages and Systems (TOPLAS)
Improving strategies via SMT solving
ESOP'11/ETAPS'11 Proceedings of the 20th European conference on Programming languages and systems: part of the joint European conferences on theory and practice of software
Widening with thresholds for programs with complex control graphs
ATVA'11 Proceedings of the 9th international conference on Automated technology for verification and analysis
Speed and precision in range analysis
SBLP'12 Proceedings of the 16th Brazilian conference on Programming Languages
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We consider a class of arithmetic equations over the complete lattice of integers (extended with -驴 and 驴) and provide a polynomial time algorithm for computing least solutions. For systems of equations with addition and least upper bounds, this algorithm is a smooth generalization of the Bellman-Ford algorithm for computing the single source shortest path in presence of positive and negative edge weights. The method then is extended to deal with more general forms of operations as well as minima with constants. For the latter, a controlled widening is applied at loops where unbounded increase occurs. We apply this algorithm to construct a cubic time algorithm for the class of interval equations using least upper bounds, addition, intersection with constant intervals as well as multiplication.