Introduction to algorithms
A practical algorithm for exact array dependence analysis
Communications of the ACM
Verification of Real-Time Systems using Linear Relation Analysis
Formal Methods in System Design - Special issue on computer aided verification (CAV 93)
ACM Transactions on Programming Languages and Systems (TOPLAS)
Proving termination with multiset orderings
Communications of the ACM
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
Comparing the Galois Connection and Widening/Narrowing Approaches to Abstract Interpretation
PLILP '92 Proceedings of the 4th International Symposium on Programming Language Implementation and Logic Programming
Synthesis of Linear Ranking Functions
TACAS 2001 Proceedings of the 7th International Conference on Tools and Algorithms for the Construction and Analysis of Systems
A Note on Abstract Interpretation Strategies for Hybrid Automata
Hybrid Systems II
Inferring Argument Size Relationships with CLP(R)
LOPSTR '96 Proceedings of the 6th International Workshop on Logic Programming Synthesis and Transformation
Possibly Not Closed Convex Polyhedra and the Parma Polyhedra Library
SAS '02 Proceedings of the 9th International Symposium on Static Analysis
Delay Analysis in Synchronous Programs
CAV '93 Proceedings of the 5th International Conference on Computer Aided Verification
Precise interprocedural analysis through linear algebra
Proceedings of the 31st ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Reasoning with infinite stable models
Artificial Intelligence
Precise widening operators for convex polyhedra
Science of Computer Programming - Special issue: Static analysis symposium (SAS 2003)
Refining the control structure of loops using static analysis
EMSOFT '09 Proceedings of the seventh ACM international conference on Embedded software
Interprocedurally analysing linear inequality relations
ESOP'07 Proceedings of the 16th European conference on Programming
Using counterexamples for improving the precision of reachability computation with polyhedra
CAV'07 Proceedings of the 19th international conference on Computer aided verification
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
Automatically refining abstract interpretations
TACAS'08/ETAPS'08 Proceedings of the Theory and practice of software, 14th international conference on Tools and algorithms for the construction and analysis of systems
Combining widening and acceleration in linear relation analysis
SAS'06 Proceedings of the 13th international conference on Static Analysis
Fixed point iteration for computing the time elapse operator
HSCC'06 Proceedings of the 9th international conference on Hybrid Systems: computation and control
CAV'06 Proceedings of the 18th international conference on Computer Aided Verification
Derivation of non-structural invariants of petri nets using abstract interpretation
ICATPN'05 Proceedings of the 26th international conference on Applications and Theory of Petri Nets
Efficient strongly relational polyhedral analysis
VMCAI'06 Proceedings of the 7th international conference on Verification, Model Checking, and Abstract Interpretation
Widening operators for weakly-relational numeric abstractions
SAS'05 Proceedings of the 12th international conference on Static Analysis
Generation of basic semi-algebraic invariants using convex polyhedra
SAS'05 Proceedings of the 12th international conference on Static Analysis
Counterexample driven refinement for abstract interpretation
TACAS'06 Proceedings of the 12th international conference on Tools and Algorithms for the Construction and Analysis of Systems
Applying abstract acceleration to (co-)reachability analysis of reactive programs
Journal of Symbolic Computation
Program analysis using symbolic ranges
SAS'07 Proceedings of the 14th international conference on Static Analysis
When the decreasing sequence fails
SAS'12 Proceedings of the 19th international conference on Static Analysis
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Convex polyhedra constitute the most used abstract domain among those capturing numerical relational information. Since the domain of convex polyhedra admits infinite ascending chains, it has to be used in conjunction with appropriate mechanisms for enforcing and accelerating convergence of the fixpoint computation.Wi dening operators provide a simple and general characterization for such mechanisms. For the domain of convex polyhedra, the original widening operator proposed by Cousot and Halbwachs amply deserves the name of standard widening since most analysis and verification tools that employ convex polyhedra also employ that operator. Nonetheless, there is an unfulfilled demand for more precise widening operators. In this paper, after a formal introduction to the standard widening where we clarify some aspects that are often overlooked, we embark on the challenging task of improving on it. We present a framework for the systematic definition of new and precise widening operators for convex polyhedra. The framework is then instantiated so as to obtain a new widening operator that combines several heuristics and uses the standard widening as a last resort so that it is never less precise. A preliminary experimental evaluation has yielded promising results.