Semantical interprocedural parallelization: an overview of the PIPS project
ICS '91 Proceedings of the 5th international conference on Supercomputing
The algorithmic analysis of hybrid systems
Theoretical Computer Science - Special issue on hybrid systems
Automatic generation of invariants and intermediate assertions
Theoretical Computer Science - Special issue: principles and practice of constraint programming
Verification of Real-Time Systems using Linear Relation Analysis
Formal Methods in System Design - Special issue on computer aided verification (CAV 93)
Verifying Temporal Properties of Reactive Systems: A STeP Tutorial
Formal Methods in System Design
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
An Algorithm Constructing the Semilinear Post* for 2-Dim Reset/Transfer VASS
MFCS '00 Proceedings of the 25th International Symposium on Mathematical Foundations of Computer Science
How to Compose Presburger-Accelerations: Applications to Broadcast Protocols
FST TCS '02 Proceedings of the 22nd Conference Kanpur on Foundations of Software Technology and Theoretical Computer Science
Cleanness Checking of String Manipulations in C Programs via Integer Analysis
SAS '01 Proceedings of the 8th International Symposium on Static Analysis
Verifying Systems with Infinite but Regular State Spaces
CAV '98 Proceedings of the 10th International Conference on Computer Aided Verification
Symbolic Verification with Periodic Sets
CAV '94 Proceedings of the 6th International Conference on Computer Aided Verification
Multiple Counters Automata, Safety Analysis and Presburger Arithmetic
CAV '98 Proceedings of the 10th International Conference on Computer Aided Verification
A static analyzer for large safety-critical software
PLDI '03 Proceedings of the ACM SIGPLAN 2003 conference on Programming language design and implementation
Decidable and Undecidable Problems in Matrix Theory
Decidable and Undecidable Problems in Matrix Theory
Precise widening operators for convex polyhedra
SAS'03 Proceedings of the 10th international conference on Static analysis
CAV'06 Proceedings of the 18th international conference on Computer Aided Verification
Program analysis as constraint solving
Proceedings of the 2008 ACM SIGPLAN conference on Programming language design and implementation
Automatic modular abstractions for linear constraints
Proceedings of the 36th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
TACAS '09 Proceedings of the 15th International Conference on Tools and Algorithms for the Construction and Analysis of Systems: Held as Part of the Joint European Conferences on Theory and Practice of Software, ETAPS 2009,
How an "incoherent behavior" inside generic hardware component characterizes functional errors
AIKED'09 Proceedings of the 8th WSEAS international conference on Artificial intelligence, knowledge engineering and data bases
Scenarios for validating systemC descriptions
ICC'08 Proceedings of the 12th WSEAS international conference on Circuits
Refining Abstract Interpretation-Based Static Analyses with Hints
APLAS '09 Proceedings of the 7th Asian Symposium on Programming Languages and Systems
Acceleration in convex data-flow analysis
FSTTCS'07 Proceedings of the 27th international conference on Foundations of software technology and theoretical computer science
Accelerated Invariant Generation for C Programs with Aspic and C2fsm
Electronic Notes in Theoretical Computer Science (ENTCS)
Abstract Fixpoint Computations with Numerical Acceleration Methods
Electronic Notes in Theoretical Computer Science (ENTCS)
Extending Abstract Acceleration Methods to Data-Flow Programs with Numerical Inputs
Electronic Notes in Theoretical Computer Science (ENTCS)
Multi-dimensional rankings, program termination, and complexity bounds of flowchart programs
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
Solving systems of rational equations through strategy iteration
ACM Transactions on Programming Languages and Systems (TOPLAS)
Improving strategies via SMT solving
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
Size invariant and ranking function synthesis in a functional language
WFLP'11 Proceedings of the 20th international conference on Functional and constraint logic programming
Logico-numerical abstract acceleration and application to the verification of data-flow programs
SAS'11 Proceedings of the 18th international conference on Static analysis
Using bounded model checking to focus fixpoint iterations
SAS'11 Proceedings of the 18th international conference on Static analysis
Widening with thresholds for programs with complex control graphs
ATVA'11 Proceedings of the 9th international conference on Automated technology for verification and analysis
Acceleration of the abstract fixpoint computation in numerical program analysis
Journal of Symbolic Computation
Applying abstract acceleration to (co-)reachability analysis of reactive programs
Journal of Symbolic Computation
SAS'07 Proceedings of the 14th international conference on Static Analysis
Program analysis using symbolic ranges
SAS'07 Proceedings of the 14th international conference on Static Analysis
Proving Termination by Policy Iteration
Electronic Notes in Theoretical Computer Science (ENTCS)
Convex Invariant Refinement by Control Node Splitting: a Heuristic Approach
Electronic Notes in Theoretical Computer Science (ENTCS)
When the decreasing sequence fails
SAS'12 Proceedings of the 19th international conference on Static Analysis
SAS'12 Proceedings of the 19th international conference on Static Analysis
Abstract acceleration of general linear loops
Proceedings of the 41st ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages
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Linear Relation Analysis [CH78, Hal79] is one of the first, but still one of the most powerful, abstract interpretations working in an infinite lattice. As such, it makes use of a widening operator to enforce the convergence of fixpoint computations. While the approximation due to widening can be arbitrarily refined by delaying the application of widening, the analysis quickly becomes too expensive with the increase of delay. Previous attempts at improving the precision of widening are not completely satisfactory, since none of them is guaranteed to improve the precision of the result, and they can nevertheless increase the cost of the analysis. In this paper, we investigate an improvement of Linear Relation Analysis consisting in computing, when possible, the exact (abstract) effect of a loop. This technique is fully compatible with the use of widening, and whenever it applies, it improves both the precision and the performance of the analysis.