Constraint propagation with interval labels
Artificial Intelligence
A technique for summarizing data access and its use in parallelism enhancing transformations
PLDI '89 Proceedings of the ACM SIGPLAN 1989 Conference on Programming language design and implementation
Timing assumptions and verification of finite-state concurrent systems
Proceedings of the international workshop on Automatic verification methods for finite state systems
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
Systematic design of program analysis frameworks
POPL '79 Proceedings of the 6th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
A New Numerical Abstract Domain Based on Difference-Bound Matrices
PADO '01 Proceedings of the Second Symposium on Programs as Data Objects
A Few Graph-Based Relational Numerical Abstract Domains
SAS '02 Proceedings of the 9th International Symposium on Static Analysis
Automatic Removal of Array Memory Leaks in Java
CC '00 Proceedings of the 9th International Conference on Compiler Construction
A static analyzer for large safety-critical software
PLDI '03 Proceedings of the ACM SIGPLAN 2003 conference on Programming language design and implementation
Efficient verification of real-time systems: compact data structure and state-space reduction
RTSS '97 Proceedings of the 18th IEEE Real-Time Systems Symposium
WCRE '01 Proceedings of the Eighth Working Conference on Reverse Engineering (WCRE'01)
Precise widening operators for convex polyhedra
Science of Computer Programming - Special issue: Static analysis symposium (SAS 2003)
Precise widening operators for convex polyhedra
SAS'03 Proceedings of the 10th international conference on Static analysis
Two variables per linear inequality as an abstract domain
LOPSTR'02 Proceedings of the 12th international conference on Logic based program synthesis and transformation
Scalable analysis of linear systems using mathematical programming
VMCAI'05 Proceedings of the 6th international conference on Verification, Model Checking, and Abstract Interpretation
Pentagons: a weakly relational abstract domain for the efficient validation of array accesses
Proceedings of the 2008 ACM symposium on Applied computing
Automatic modular abstractions for linear constraints
Proceedings of the 36th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
ACM Computing Surveys (CSUR)
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
Formal Methods in System Design
A minimalistic look at widening operators
Higher-Order and Symbolic Computation
An improved tight closure algorithm for integer octagonal constraints
VMCAI'08 Proceedings of the 9th international conference on Verification, model checking, and abstract interpretation
Pentagons: A weakly relational abstract domain for the efficient validation of array accesses
Science of Computer Programming
Widening and narrowing operators for abstract interpretation
Computer Languages, Systems and Structures
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We discuss the construction of proper widening operators on several weakly-relational numeric abstractions. Our proposal differs from previous ones in that we actually consider the semantic abstract domains, whose elements are geometric shapes, instead of the (more concrete) syntactic abstract domains of constraint networks and matrices. Since the closure by entailment operator preserves geometric shapes, but not their syntactic expressions, our widenings are immune from the divergence issues that could be faced by the previous approaches when interleaving the applications of widening and closure. The new widenings, which are variations of the standard widening for convex polyhedra defined by Cousot and Halbwachs, can be made as precise as the previous proposals working on the syntactic domains. The implementation of each new widening relies on the availability of an effective reduction procedure for the considered constraint description: we provide such an algorithm for the domain of octagonal shapes.