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Refining Model Checking by Abstract Interpretation
Automated Software Engineering
Combining Forward and Backward Analyses of Temporal Properties
PADO '01 Proceedings of the Second Symposium on Programs as Data Objects
Partial Completeness of Abstract Fixpoint Checking
SARA '02 Proceedings of the 4th International Symposium on Abstraction, Reformulation, and Approximation
Incremental Verification by Abstraction
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Relative Completeness of Abstraction Refinement for Software Model Checking
TACAS '02 Proceedings of the 8th International Conference on Tools and Algorithms for the Construction and Analysis of Systems
Incompleteness, Counterexamples, and Refinements in Abstract Model-Checking
SAS '01 Proceedings of the 8th International Symposium on Static Analysis
Modular verification of software components in C
Proceedings of the 25th International Conference on Software Engineering
General decidability theorems for infinite-state systems
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Counterexample-guided abstraction refinement for symbolic model checking
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ICATPN'07 Proceedings of the 28th international conference on Applications and theory of Petri nets and other models of concurrency
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Fixpoint Guided Abstraction Refinement for Alternating Automata
CIAA '09 Proceedings of the 14th International Conference on Implementation and Application of Automata
Formal Methods in System Design
Approximation refinement for interpolation-based model checking
VMCAI'08 Proceedings of the 9th international conference on Verification, model checking, and abstract interpretation
A forward-backward abstraction refinement algorithm
VMCAI'08 Proceedings of the 9th international conference on Verification, model checking, and abstract interpretation
Fixed point guided abstraction refinement for alternating automata
Theoretical Computer Science
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ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming: Part II
Thread-modular counterexample-guided abstraction refinement
SAS'10 Proceedings of the 17th international conference on Static analysis
Constrained monotonic abstraction: a CEGAR for parameterized verification
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Non-monotonic refinement of control abstraction for concurrent programs
ATVA'10 Proceedings of the 8th international conference on Automated technology for verification and analysis
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CAV'13 Proceedings of the 25th international conference on Computer Aided Verification
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In this paper, we present an abstract fixpoint checking algorithm with automatic refinement by backward completion in Moore closed abstract domains. We study the properties of our algorithm and prove it to be more precise than the counterexample guided abstract refinement algorithm (CEGAR). Contrary to several works in the literature, our algorithm does not require the abstract domains to be partitions of the state space. We also show that our automatic refinement technique is compatible with so-called acceleration techniques. Furthermore, the use of Boolean closed domains does not improve the precision of our algorithm. The algorithm is illustrated by proving properties of programs with nested loops.