Heuristics: intelligent search strategies for computer problem solving
Heuristics: intelligent search strategies for computer problem solving
Modeling and analysis of stochastic systems
Modeling and analysis of stochastic systems
Model-checking continuous-time Markov chains
ACM Transactions on Computational Logic (TOCL)
Data Structures and Algorithms in Java
Data Structures and Algorithms in Java
TACAS '00 Proceedings of the 6th International Conference on Tools and Algorithms for Construction and Analysis of Systems: Held as Part of the European Joint Conferences on the Theory and Practice of Software, ETAPS 2000
Probabilistic Verification of Discrete Event Systems Using Acceptance Sampling
CAV '02 Proceedings of the 14th International Conference on Computer Aided Verification
On the Use of Model Checking Techniques for Dependability Evaluation
SRDS '00 Proceedings of the 19th IEEE Symposium on Reliable Distributed Systems
Model-Checking Algorithms for Continuous-Time Markov Chains
IEEE Transactions on Software Engineering
Directed explicit-state model checking in the validation of communication protocols
International Journal on Software Tools for Technology Transfer (STTT)
QEST '05 Proceedings of the Second International Conference on the Quantitative Evaluation of Systems
Spin model checker, the: primer and reference manual
Spin model checker, the: primer and reference manual
Counterexamples for timed probabilistic reachability
FORMATS'05 Proceedings of the Third international conference on Formal Modeling and Analysis of Timed Systems
TACAS'05 Proceedings of the 11th international conference on Tools and Algorithms for the Construction and Analysis of Systems
On statistical model checking of stochastic systems
CAV'05 Proceedings of the 17th international conference on Computer Aided Verification
PRISM: a tool for automatic verification of probabilistic systems
TACAS'06 Proceedings of the 12th international conference on Tools and Algorithms for the Construction and Analysis of Systems
Quantitative verification: models techniques and tools
Proceedings of the the 6th joint meeting of the European software engineering conference and the ACM SIGSOFT symposium on The foundations of software engineering
Quantitative verification: models, techniques and tools
The 6th Joint Meeting on European software engineering conference and the ACM SIGSOFT symposium on the foundations of software engineering: companion papers
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
Survey on Directed Model Checking
Model Checking and Artificial Intelligence
Significant Diagnostic Counterexamples in Probabilistic Model Checking
HVC '08 Proceedings of the 4th International Haifa Verification Conference on Hardware and Software: Verification and Testing
Counterexamples in Probabilistic LTL Model Checking for Markov Chains
CONCUR 2009 Proceedings of the 20th International Conference on Concurrency Theory
Counterexamples in probabilistic model checking
TACAS'07 Proceedings of the 13th international conference on Tools and algorithms for the construction and analysis of systems
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
Conditional probabilities over probabilistic and nondeterministic systems
TACAS'08/ETAPS'08 Proceedings of the Theory and practice of software, 14th international conference on Tools and algorithms for the construction and analysis of systems
Proceedings of the 2010 ICSE Workshop on Quantitative Stochastic Models in the Verification and Design of Software Systems
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Current numerical model checkers for stochastic systems can efficiently analyse stochastic models. However, the fact that they are unable to provide debugging information constrains their practical use. In precursory work we proposed a method to select diagnostic traces, in the parlance of functional model checking commonly referred to as failure traces or counterexamples, for probabilistic timed reachability properties on discrete-time and continuous-time Markov chains. We applied directed explicit-state search algorithms, like Z∗, to determine a diagnostic trace which carries large amount of probability. In this paper we extend this approach to determining sets of traces that carry large probability mass, since properties of stochastic systems are typically not violated by single traces, but by collections of those. To this end we extend existing heuristics guided search algorithms so that they select sets of traces. The result is provided in the form of a Markov chain. Such diagnostic Markov chains are not just essential tools for diagnostics and debugging but, they also allow the solution of timed reachability probability to be approximated from below. In particular cases, they also provide real counterexamples which can be used to show the violation of the given property. Our algorithms have been implemented in the stochastic model checker PRISM. We illustrate the applicability of our approach using a number of case studies.