Abstract interpretation and application to logic programs
Journal of Logic 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
A unified approach to global program optimization
POPL '73 Proceedings of the 1st annual ACM SIGACT-SIGPLAN symposium on Principles of programming languages
POPL '77 Proceedings of the 4th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Improving the Results of Static Analyses Programs by Local Decreasing Iteration
Proceedings of the 12th Conference on Foundations of Software Technology and Theoretical Computer Science
A static analyzer for large safety-critical software
PLDI '03 Proceedings of the ACM SIGPLAN 2003 conference on Programming language design and implementation
WCRE '01 Proceedings of the Eighth Working Conference on Reverse Engineering (WCRE'01)
Semantics-based program analysis via symbolic composition of transfer relations
Semantics-based program analysis via symbolic composition of transfer relations
Two variables per linear inequality as an abstract domain
LOPSTR'02 Proceedings of the 12th international conference on Logic based program synthesis and transformation
Proving the absence of run-time errors in safety-critical avionics code
EMSOFT '07 Proceedings of the 7th ACM & IEEE international conference on Embedded software
The Verification Grand Challenge and Abstract Interpretation
Verified Software: Theories, Tools, Experiments
Inferring Min and Max Invariants Using Max-Plus Polyhedra
SAS '08 Proceedings of the 15th international symposium on Static Analysis
The Zonotope Abstract Domain Taylor1+
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
Formal Methods in System Design
A minimalistic look at widening operators
Higher-Order and Symbolic Computation
Precise fixpoint computation through strategy iteration
ESOP'07 Proceedings of the 16th European conference on Programming
Combination of abstractions in the ASTRÉE static analyzer
ASIAN'06 Proceedings of the 11th Asian computing science conference on Advances in computer science: secure software and related issues
The Interval Analysis of Multilinear Expressions
Electronic Notes in Theoretical Computer Science (ENTCS)
SMT-AI: an Abstract Interpreter as Oracle for k-induction
Electronic Notes in Theoretical Computer Science (ENTCS)
Electronic Notes in Theoretical Computer Science (ENTCS)
A Note on the Inversion Join for Polyhedral Analysis
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 contract checking with abstract interpretation
FoVeOOS'10 Proceedings of the 2010 international conference on Formal verification of object-oriented software
Generalizing the template polyhedral domain
ESOP'11/ETAPS'11 Proceedings of the 20th European conference on Programming languages and systems: part of the joint European conferences on theory and practice of software
The two variable per inequality abstract domain
Higher-Order and Symbolic Computation
Using bounded model checking to focus fixpoint iterations
SAS'11 Proceedings of the 18th international conference on Static analysis
Policy iteration within logico-numerical abstract domains
ATVA'11 Proceedings of the 9th international conference on Automated technology for verification and analysis
An abstract domain to discover interval linear equalities
VMCAI'10 Proceedings of the 11th international conference on Verification, Model Checking, and Abstract Interpretation
Discovering invariants via simple component analysis
Journal of Symbolic Computation
Inferring Sufficient Conditions with Backward Polyhedral Under-Approximations
Electronic Notes in Theoretical Computer Science (ENTCS)
Stratified Static Analysis Based on Variable Dependencies
Electronic Notes in Theoretical Computer Science (ENTCS)
PAGAI: A Path Sensitive Static Analyser
Electronic Notes in Theoretical Computer Science (ENTCS)
Abstract acceleration of general linear loops
Proceedings of the 41st ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages
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We present lightweight and generic symbolic methods to improve the precision of numerical static analyses based on Abstract Interpretation. The main idea is to simplify numerical expressions before they are fed to abstract transfer functions. An important novelty is that these simplifications are performed on-the-fly, using information gathered dynamically by the analyzer. A first method, called “linearization,” allows abstracting arbitrary expressions into affine forms with interval coefficients while simplifying them. A second method, called “symbolic constant propagation,” enhances the simplification feature of the linearization by propagating assigned expressions in a symbolic way. Combined together, these methods increase the relationality level of numerical abstract domains and make them more robust against program transformations. We show how they can be integrated within the classical interval, octagon and polyhedron domains. These methods have been incorporated within the Astrée static analyzer that checks for the absence of run-time errors in embedded critical avionics software. We present an experimental proof of their usefulness.