Analysis of Linear Hybrid Systems in CLP
Logic-Based Program Synthesis and Transformation
Theoretical Computer Science
Exact join detection for convex polyhedra and other numerical abstractions
Computational Geometry: Theory and Applications
Weakly-relational shapes for numeric abstractions: improved algorithms and proofs of correctness
Formal Methods in System Design
Grids: a domain for analyzing the distribution of numerical values
LOPSTR'06 Proceedings of the 16th international conference on Logic-based program synthesis and transformation
Widening and narrowing operators for abstract interpretation
Computer Languages, Systems and Structures
Quadtrees as an Abstract Domain
Electronic Notes in Theoretical Computer Science (ENTCS)
BOXES: a symbolic abstract domain of boxes
SAS'10 Proceedings of the 17th international conference on Static analysis
On the consistency, expressiveness, and precision of partial modeling formalisms
Information and Computation
Using bounded model checking to focus fixpoint iterations
SAS'11 Proceedings of the 18th international conference on Static analysis
Donut domains: efficient non-convex domains for abstract interpretation
VMCAI'12 Proceedings of the 13th international conference on Verification, Model Checking, and Abstract Interpretation
Ideal abstractions for well-structured transition systems
VMCAI'12 Proceedings of the 13th international conference on Verification, Model Checking, and Abstract Interpretation
A new look at the automatic synthesis of linear ranking functions
Information and Computation
SAS'12 Proceedings of the 19th international conference on Static Analysis
SAS'12 Proceedings of the 19th international conference on Static Analysis
Dynamic enforcement of knowledge-based security policies using probabilistic abstract interpretation
Journal of Computer Security
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The finite powerset construction upgrades an abstract domain by allowing for the representation of finite disjunctions of its elements. While most of the operations on the finite powerset abstract domain are easily obtained by “lifting” the corresponding operations on the base-level domain, the problem of endowing finite powersets with a provably correct widening operator is still open. In this paper we define three generic widening methodologies for the finite powerset abstract domain. The widenings are obtained by lifting any widening operator defined on the base-level abstract domain and are parametric with respect to the specification of a few additional operators that allow all the flexibility required to tune the complexity/precision trade-off. As far as we know, this is the first time that the problem of deriving non-trivial, provably correct widening operators in a domain refinement is tackled successfully. We illustrate the proposed techniques by instantiating our widening methodologies on powersets of convex polyhedra, a domain for which no non-trivial widening operator was previously known.