Graph-Based Algorithms for Boolean Function Manipulation
IEEE Transactions on Computers
Abstract interpretation and application to logic programs
Journal of Logic Programming
Verification of Real-Time Systems using Linear Relation Analysis
Formal Methods in System Design - Special issue on computer aided verification (CAV 93)
Higher-Order and Symbolic Computation
Relational inductive shape analysis
Proceedings of the 35th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
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
Some Experience on the Software Engineering of Abstract Interpretation Tools
Electronic Notes in Theoretical Computer Science (ENTCS)
Scalable analysis of linear systems using mathematical programming
VMCAI'05 Proceedings of the 6th international conference on Verification, Model Checking, and Abstract Interpretation
Symbolic methods to enhance the precision of numerical abstract domains
VMCAI'06 Proceedings of the 7th international conference on Verification, Model Checking, and Abstract Interpretation
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
ESOP'10 Proceedings of the 19th European conference on Programming Languages and Systems
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Policy Iteration is an algorithm for the exact solving of optimization and game theory problems, formulated as equations on min max affine expressions. It has been shown that the problem of finding the least fixpoint of semantic equations on some abstract domains can be reduced to such optimization problems. This enables the use of Policy Iteration to solve such equations, instead of the traditional Kleene iteration that performs approximations to ensure convergence. We first show in this paper that the concept of Policy Iteration can be integrated into numerical abstract domains in a generic way. This allows to widen considerably its applicability in static analysis. We then consider the verification of programs manipulating Boolean and numerical variables, and we provide an efficient method to integrate the concept of policy in a logico-numerical abstract domain that mixes Boolean and numerical properties. Our experiments show the benefit of our approach compared to a naive application of Policy Iteration to such programs.