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
Introduction to Mathematical Theory of Computation
Introduction to Mathematical Theory of Computation
A New Numerical Abstract Domain Based on Difference-Bound Matrices
PADO '01 Proceedings of the Second Symposium on Programs as Data Objects
Possibly Not Closed Convex Polyhedra and the Parma Polyhedra Library
SAS '02 Proceedings of the 9th International Symposium on Static Analysis
Polyhedral Analysis for Synchronous Languages
SAS '99 Proceedings of the 6th International Symposium on Static Analysis
CSSV: towards a realistic tool for statically detecting all buffer overflows in C
PLDI '03 Proceedings of the ACM SIGPLAN 2003 conference on Programming language design and implementation
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
Theoretical Computer Science
Static analysis by policy iteration on relational domains
ESOP'07 Proceedings of the 16th European conference on Programming
Interprocedurally analysing linear inequality relations
ESOP'07 Proceedings of the 16th European conference on Programming
An abstract interpretation based combinator for modelling while loops in constraint programming
CP'07 Proceedings of the 13th international conference on Principles and practice of constraint programming
A Note on the Inversion Join for Polyhedral Analysis
Electronic Notes in Theoretical Computer Science (ENTCS)
Interval slopes as a numerical abstract domain for floating-point variables
SAS'10 Proceedings of the 17th international conference on Static analysis
Simple and precise widenings for H-polyhedra
APLAS'10 Proceedings of the 8th Asian conference on Programming languages and systems
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
Static analysis in disjunctive numerical domains
SAS'06 Proceedings of the 13th international conference on Static Analysis
Static analysis of numerical algorithms
SAS'06 Proceedings of the 13th international conference on Static Analysis
Widening polyhedra with landmarks
APLAS'06 Proceedings of the 4th Asian conference on Programming Languages and Systems
ESOP'10 Proceedings of the 19th European conference on Programming Languages and Systems
A generic ellipsoid abstract domain for linear time invariant systems
Proceedings of the 15th ACM international conference on Hybrid Systems: Computation and Control
Random: r-based analyzer for numerical domains
LPAR'12 Proceedings of the 18th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
Abstract interpretation meets convex optimization
Journal of Symbolic Computation
Tropical linear-fractional programming and parametric mean payoff games
Journal of Symbolic Computation
The gauge domain: scalable analysis of linear inequality invariants
CAV'12 Proceedings of the 24th international conference on Computer Aided Verification
Program analysis using symbolic ranges
SAS'07 Proceedings of the 14th international conference on Static Analysis
The Abstract Domain of Parallelotopes
Electronic Notes in Theoretical Computer Science (ENTCS)
Polyhedral analysis using parametric objectives
SAS'12 Proceedings of the 19th international conference on Static Analysis
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Polyhedral analysis infers invariant linear equalities and inequalities of imperative programs. However, the exponential complexity of polyhedral operations such as image computation and convex hull limits the applicability of polyhedral analysis. Weakly relational domains such as intervals and octagons address the scalability issue by considering polyhedra whose constraints are drawn from a restricted, user-specified class. On the other hand, these domains rely solely on candidate expressions provided by the user. Therefore, they often fail to produce strong invariants. We propose a polynomial time approach to strongly relational analysis. We provide efficient implementations of join and post condition operations, achieving a trade off between performance and accuracy. We have implemented a strongly relational polyhedral analyzer for a subset of the C language. Initial experimental results on benchmark examples are encouraging.