Proceedings of the 2010 ICSE Workshop on Quantitative Stochastic Models in the Verification and Design of Software Systems
Counterexample generation for Markov chains using SMT-based bounded model checking
FMOODS'11/FORTE'11 Proceedings of the joint 13th IFIP WG 6.1 and 30th IFIP WG 6.1 international conference on Formal techniques for distributed systems
DiPro: a tool for probabilistic counterexample generation
Proceedings of the 18th international SPIN conference on Model checking software
From probabilistic counterexamples via causality to fault trees
SAFECOMP'11 Proceedings of the 30th international conference on Computer safety, reliability, and security
K*: A heuristic search algorithm for finding the k shortest paths
Artificial Intelligence
Hierarchical counterexamples for discrete-time Markov chains
ATVA'11 Proceedings of the 9th international conference on Automated technology for verification and analysis
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
Refinement and difference for probabilistic automata
QEST'13 Proceedings of the 10th international conference on Quantitative Evaluation of Systems
High-Level counterexamples for probabilistic automata
QEST'13 Proceedings of the 10th international conference on Quantitative Evaluation of Systems
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Current stochastic model checkers do not make counterexamples for property violations readily available. In this paper, we apply directed explicit state-space search to discrete and continuous-time Markov chains in order to compute counterexamples for the violation of PCTL or CSL properties. Directed explicit state-space search algorithms explore the state space on-the-fly, which makes our method very efficient and highly scalable. They can also be guided using heuristics which usually improve the performance of the method. Counterexamples provided by our method have two important properties. First, they include those traces which contribute the greatest amount of probability to the property violation. Hence, they show the most probable offending execution scenarios of the system. Second, the obtained counterexamples tend to be small. Hence, they can be effectively analyzed by a human user. Both properties make the counterexamples obtained by our method very useful for debugging purposes. We implemented our method based on the stochastic model checker PRISM and applied it to a number of case studies in order to illustrate its applicability.