Counterexample Generation for Discrete-Time Markov Chains Using Bounded Model Checking
VMCAI '09 Proceedings of the 10th International Conference on Verification, Model Checking, and Abstract Interpretation
Probabilistic Reachability for Parametric Markov Models
Proceedings of the 16th International SPIN Workshop on Model Checking Software
Counterexamples in Probabilistic LTL Model Checking for Markov Chains
CONCUR 2009 Proceedings of the 20th International Conference on Concurrency Theory
Proceedings of the 2010 ICSE Workshop on Quantitative Stochastic Models in the Verification and Design of Software Systems
Computing the leakage of information-hiding systems
TACAS'10 Proceedings of the 16th international conference on Tools and Algorithms for the Construction and Analysis of Systems
| Hi-index | 0.00 |
Counterexamples for probabilistic reachability in Markov chains are sets of paths that all reach a goal state and whose cumulative likelihood exceeds a threshold. This paper is concerned with the issue of how to conveniently represent these sets. Experiments, partially substantiated with combinatorial arguments, show that the cardinality of such sets may be excessive. To obtain compact representations of counterexamples we suggest to use regular expressions. We present a simple algorithm to generate minimal regular expressions and adopt a recursive scheme to determine their likelihood. Markov chain reduction prior to counter example generation may yield even shorter regular expressions. The feasibility of the approach is illustrated by means two protocols: leader election and the Crowds protocol.