Static analysis of linear congruence equalities among variables of a program
TAPSOFT '91 Proceedings of the international joint conference on theory and practice of software development on Colloquium on trees in algebra and programming (CAAP '91): vol 1
Array abstractions using semantic analysis of trapezoid congruences
ICS '92 Proceedings of the 6th international conference on Supercomputing
A hierarchy of constraint systems for data-flow analysis of constraint logic-based languages
Science of Computer Programming - Special issue on concurrent constraint programming
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
WCRE '01 Proceedings of the Eighth Working Conference on Reverse Engineering (WCRE'01)
Inner and outer approximations of polytopes using boxes
Computational Geometry: Theory and Applications
Not necessarily closed convex polyhedra and the double description method
Formal Aspects of Computing
Widening operators for powerset domains
International Journal on Software Tools for Technology Transfer (STTT) - A View from Formal Methods 2003 (pp 301-354); Special Section on Recent Advances in Hardware Verification (pp 355-447)
Inferring Min and Max Invariants Using Max-Plus Polyhedra
SAS '08 Proceedings of the 15th international symposium on Static Analysis
Generating and Analyzing Symbolic Traces of Simulink/Stateflow Models
CAV '09 Proceedings of the 21st International Conference on Computer Aided Verification
The Zonotope Abstract Domain Taylor1+
CAV '09 Proceedings of the 21st International Conference on Computer Aided Verification
Apron: A Library of Numerical Abstract Domains for Static Analysis
CAV '09 Proceedings of the 21st International Conference on Computer Aided Verification
Interval Polyhedra: An Abstract Domain to Infer Interval Linear Relationships
SAS '09 Proceedings of the 16th International Symposium on Static Analysis
Exact join detection for convex polyhedra and other numerical abstractions
Computational Geometry: Theory and Applications
An abstract domain extending difference-bound matrices with disequality constraints
VMCAI'07 Proceedings of the 8th international conference on Verification, model checking, and abstract interpretation
BOXES: a symbolic abstract domain of boxes
SAS'10 Proceedings of the 17th international conference on Static analysis
Interprocedural exception analysis for C++
Proceedings of the 25th European conference on Object-oriented programming
Static analysis of numerical algorithms
SAS'06 Proceedings of the 13th international conference on Static Analysis
VMCAI'05 Proceedings of the 6th international conference on Verification, Model Checking, and Abstract Interpretation
A logical product approach to zonotope intersection
CAV'10 Proceedings of the 22nd international conference on Computer Aided Verification
ESOP'10 Proceedings of the 19th European conference on Programming Languages and Systems
Convexity recognition of the union of polyhedra
Computational Geometry: Theory and Applications
Under-approximations of computations in real numbers based on generalized affine arithmetic
SAS'07 Proceedings of the 14th international conference on Static Analysis
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Program analysis using abstract interpretation has been successfully applied in practice to find runtime bugs or prove software correct. Most abstract domains that are used widely rely on convexity for their scalability. However, the ability to express non-convex properties is sometimes required in order to achieve a precise analysis of some numerical properties. This work combines already known abstract domains in a novel way in order to design new abstract domains that tackle some non-convex invariants. The abstract objects of interest are encoded as a pair of two convex abstract objects: the first abstract object defines an over-approximation of the possible reached values, as is done customarily. The second abstract object under-approximates the set of impossible values within the state-space of the first abstract object. Therefore, the geometrical concretization of our objects is defined by a convex set minus another convex set (or hole). We thus call these domains donut domains .