Verification of Real-Time Systems using Linear Relation Analysis
Formal Methods in System Design - Special issue on computer aided verification (CAV 93)
Automatic discovery of linear restraints among variables of a program
POPL '78 Proceedings of the 5th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
POPL '77 Proceedings of the 4th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Asserting the Precision of Floating-Point Computations: A Simple Abstract Interpreter
ESOP '02 Proceedings of the 11th European Symposium on Programming Languages and Systems
Comparing the Galois Connection and Widening/Narrowing Approaches to Abstract Interpretation
PLILP '92 Proceedings of the 4th International Symposium on Programming Language Implementation and Logic Programming
Computing polynomial program invariants
Information Processing Letters
Higher-Order and Symbolic Computation
Generating all polynomial invariants in simple loops
Journal of Symbolic Computation
FAST: acceleration from theory to practice
International Journal on Software Tools for Technology Transfer (STTT)
Apron: A Library of Numerical Abstract Domains for Static Analysis
CAV '09 Proceedings of the 21st International Conference on Computer Aided Verification
Static analysis by policy iteration on relational domains
ESOP'07 Proceedings of the 16th European conference on Programming
Static analysis of the accuracy in control systems: principles and experiments
FMICS'07 Proceedings of the 12th international conference on Formal methods for industrial critical systems
Abstract Fixpoint Computations with Numerical Acceleration Methods
Electronic Notes in Theoretical Computer Science (ENTCS)
Extending Abstract Acceleration Methods to Data-Flow Programs with Numerical Inputs
Electronic Notes in Theoretical Computer Science (ENTCS)
Static analysis of finite precision computations
VMCAI'11 Proceedings of the 12th international conference on Verification, model checking, and abstract interpretation
Static analysis of numerical algorithms
SAS'06 Proceedings of the 13th international conference on Static Analysis
Combining widening and acceleration in linear relation analysis
SAS'06 Proceedings of the 13th international conference on Static Analysis
Scalable analysis of linear systems using mathematical programming
VMCAI'05 Proceedings of the 6th international conference on Verification, Model Checking, and Abstract Interpretation
CAV'06 Proceedings of the 18th international conference on Computer Aided Verification
Compositional analysis of floating-point linear numerical filters
CAV'05 Proceedings of the 17th international conference on Computer Aided Verification
A policy iteration algorithm for computing fixed points in static analysis of programs
CAV'05 Proceedings of the 17th international conference on Computer Aided Verification
Widening polyhedra with landmarks
APLAS'06 Proceedings of the 4th Asian conference on Programming Languages and Systems
Accelerated data-flow analysis
SAS'07 Proceedings of the 14th international conference on Static Analysis
SAS'07 Proceedings of the 14th international conference on Static Analysis
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Static analysis by abstract interpretation aims at automatically proving properties of computer programs, by computing invariants that over-approximate the program behaviors. These invariants are defined as the least fixpoint of a system of semantic equations and are most often computed using the Kleene iteration. This computation may not terminate so specific solutions were proposed to deal with this issue. Most of the proposed methods sacrifice the precision of the solution to guarantee the termination of the computation in a finite number of iterations. In this article, we define a new method which allows to obtain a precise fixpoint in a short time. The main idea is to use numerical methods designed for accelerating the convergence of numerical sequences. These methods were primarily designed to transform a convergent, real valued sequence into another sequence that converges faster to the same limit. In this article, we show how they can be integrated into the Kleene iteration in order to improve the fixpoint computation in the abstract interpretation framework. An interesting feature of our method is that it remains very close to the Kleene iteration and thus can be easily implemented in existing static analyzers. We describe a general framework and its application to two numerical abstract domains: the interval domain and the octagon domain. Experimental results show that the number of iterations and the time needed to compute the fixpoint undergo a significant reduction compared to the Kleene iteration, while its precision is preserved.