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Computers and Intractability: A Guide to the Theory of NP-Completeness
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Tree-Like Counterexamples in Model Checking
LICS '02 Proceedings of the 17th Annual IEEE Symposium on Logic in Computer Science
Reduction and Refinement Strategies for Probabilistic Analysis
PAPM-PROBMIV '02 Proceedings of the Second Joint International Workshop on Process Algebra and Probabilistic Methods, Performance Modeling and Verification
Reachability Analysis of Probabilistic Systems by Successive Refinements
PAPM-PROBMIV '01 Proceedings of the Joint International Workshop on Process Algebra and Probabilistic Methods, Performance Modeling and Verification
Reduction and Refinement Strategies for Probabilistic Analysis
PAPM-PROBMIV '02 Proceedings of the Second Joint International Workshop on Process Algebra and Probabilistic Methods, Performance Modeling and Verification
Incremental Verification by Abstraction
TACAS 2001 Proceedings of the 7th International Conference on Tools and Algorithms for the Construction and Analysis of Systems
Probabilistic Simulations for Probabilistic Processes
CONCUR '94 Proceedings of the Concurrency Theory
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LICS '00 Proceedings of the 15th Annual IEEE Symposium on Logic in Computer Science
Using Counter Example Guided Abstraction Refinement to Find Complex Bugs
Proceedings of the conference on Design, automation and test in Europe - Volume 1
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Abstract interpretation of programs as Markov decision processes
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Theoretical Computer Science - Quantitative aspects of programming languages (QAPL 2004)
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QEST '06 Proceedings of the 3rd international conference on the Quantitative Evaluation of Systems
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ACM Transactions on Computational Logic (TOCL)
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QEST '07 Proceedings of the Fourth International Conference on Quantitative Evaluation of Systems
CAV '08 Proceedings of the 20th international conference on Computer Aided Verification
Abstraction Refinement for Probabilistic Software
VMCAI '09 Proceedings of the 10th International Conference on Verification, Model Checking, and Abstract Interpretation
Comparative branching-time semantics for Markov chains
Information and Computation
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TACAS'07 Proceedings of the 13th international conference on Tools and algorithms for the construction and analysis of systems
Flow faster: efficient decision algorithms for probabilistic simulations
TACAS'07 Proceedings of the 13th international conference on Tools and algorithms for the construction and analysis of systems
Multiple-counterexample guided iterative abstraction refinement: an industrial evaluation
TACAS'03 Proceedings of the 9th international conference on Tools and algorithms for the construction and analysis of systems
Three-valued abstraction for continuous-time Markov chains
CAV'07 Proceedings of the 19th international conference on Computer aided verification
Magnifying-lens abstraction for Markov decision processes
CAV'07 Proceedings of the 19th international conference on Computer aided verification
Providing evidence of likely being on time: counterexample generation for CTMC model checking
ATVA'07 Proceedings of the 5th international conference on Automated technology for verification and analysis
Counterexamples for timed probabilistic reachability
FORMATS'05 Proceedings of the Third international conference on Formal Modeling and Analysis of Timed Systems
Abstraction refinement for termination
SAS'05 Proceedings of the 12th international conference on Static Analysis
Probability and nondeterminism in operational models of concurrency
CONCUR'06 Proceedings of the 17th international conference on Concurrency Theory
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TACAS'06 Proceedings of the 12th international conference on Tools and Algorithms for the Construction and Analysis of Systems
Don’t know in probabilistic systems
SPIN'06 Proceedings of the 13th international conference on Model Checking Software
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Formal Methods in System Design
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FORMATS'10 Proceedings of the 8th international conference on Formal modeling and analysis of timed systems
Minimal critical subsystems for discrete-time markov models
TACAS'12 Proceedings of the 18th international conference on Tools and Algorithms for the Construction and Analysis of Systems
Learning Probabilistic Systems from Tree Samples
LICS '12 Proceedings of the 2012 27th Annual IEEE/ACM Symposium on Logic in Computer Science
Assume-guarantee abstraction refinement for probabilistic systems
CAV'12 Proceedings of the 24th international conference on Computer Aided Verification
Refinement and difference for probabilistic automata
QEST'13 Proceedings of the 10th international conference on Quantitative Evaluation of Systems
Bayesian statistical model checking with application to Stateflow/Simulink verification
Formal Methods in System Design
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The main challenge in using abstractions effectively is to construct a suitable abstraction for the system being verified. One approach that tries to address this problem is that of counterexample guided abstraction refinement (CEGAR), wherein one starts with a coarse abstraction of the system, and progressively refines it, based on invalid counterexamples seen in prior model checking runs, until either an abstraction proves the correctness of the system or a valid counterexample is generated. While CEGAR has been successfully used in verifying nonprobabilistic systems automatically, CEGAR has only recently been investigated in the context of probabilistic systems. The main issues that need to be tackled in order to extend the approach to probabilistic systems is a suitable notion of “counterexample”, algorithms to generate counterexamples, check their validity, and then automatically refine an abstraction based on an invalid counterexample. In this article, we address these issues, and present a CEGAR framework for Markov decision processes.