Counterexample-guided abstraction refinement

The main practical problem in model checking is the combinatorial explosion of system states commonly known as the state explosion problem. Abstraction methods attempt to reduce the size of the state space by employing knowledge about the system and the specification in order to model only relevant features in the Kripke structure. Counterexample-guided abstraction refinement is an automatic abstraction method where, starting with a relatively small skeletal representation of the system to be verified, increasingly precise abstract representations of the system are computed. The key step is to extract information from false negatives ("spurious counterexamples") due to over-approximation.

[1]  C. Freund.  Incompleteness , 1888, The Hospital.

[2]  Patrick Cousot,et al.  Abstract interpretation: a unified lattice model for static analysis of programs by construction or approximation of fixpoints , 1977, POPL.

[3]  D. E. Long,et al.  Model checking and abstraction , 1992, POPL '92.

[4]  Alberto L. Sangiovanni-Vincentelli,et al.  An Iterative Approach to Language Containment , 1993, CAV.

[5]  Hassen Saïdi,et al.  Construction of Abstract State Graphs with PVS , 1997, CAV.

[6]  Helmut Veith,et al.  Progress on the State Explosion Problem in Model Checking , 2001, Informatics.

[7]  David L. Dill,et al.  Successive approximation of abstract transition relations , 2001, Proceedings 16th Annual IEEE Symposium on Logic in Computer Science.

[8]  Yassine Lakhnech,et al.  Incremental Verification by Abstraction , 2001, TACAS.

[9]  R. Giacobazzi,et al.  Incompleteness, Counterexamples, and Refinements in Abstract Model-Checking , 2001, SAS.

[10]  Daniel Geist,et al.  Symbolic Localization Reduction with Reconstruction Layering and Backtracking , 2002, CAV.

[11]  Ofer Strichman,et al.  SAT Based Abstraction-Refinement Using ILP and Machine Learning Techniques , 2002, CAV.

[12]  D. Dill,et al.  Counter-Example Based Predicate Discovery in Predicate Abstraction , 2002, FMCAD.

[13]  Helmut Veith,et al.  Tree-like counterexamples in model checking , 2002, Proceedings 17th Annual IEEE Symposium on Logic in Computer Science.

[14]  Sriram K. Rajamani,et al.  Generating Abstract Explanations of Spurious Counterexamples in C Programs , 2002 .

[15]  Edmund M. Clarke,et al.  Counterexample-Guided Abstraction Refinement , 2000, CAV.

[16]  Moshe Y. Vardi,et al.  Multiple-Counterexample Guided Iterative Abstraction Refinement: An Industrial Evaluation , 2003, TACAS.

[17]  Thomas A. Henzinger,et al.  Counterexample-Guided Control , 2003, ICALP.

[18]  Olaf Stursberg,et al.  Verification of Hybrid Systems Based on Counterexample-Guided Abstraction Refinement , 2003, TACAS.