Handbook of theoretical computer science (vol. B)
The complexity of probabilistic verification
Journal of the ACM (JACM)
Introduction to Algorithms
A Comparative Study of Symbolic Algorithms for the Computation of Fair Cycles
FMCAD '00 Proceedings of the Third International Conference on Formal Methods in Computer-Aided Design
Temporal Logics for the Specification of Performance and Reliability
STACS '97 Proceedings of the 14th Annual Symposium on Theoretical Aspects of Computer Science
CONCUR 2005 - Concurrency Theory
Temporal Logics and Model Checking for Fairly Correct Systems
LICS '06 Proceedings of the 21st Annual IEEE Symposium on Logic in Computer Science
The temporal logic of programs
SFCS '77 Proceedings of the 18th Annual Symposium on Foundations of Computer Science
Automatic verification of probabilistic concurrent finite state programs
SFCS '85 Proceedings of the 26th Annual Symposium on Foundations of Computer Science
Regular Expressions for PCTL Counterexamples
QEST '08 Proceedings of the 2008 Fifth International Conference on Quantitative Evaluation of Systems
Debugging of Dependability Models Using Interactive Visualization of Counterexamples
QEST '08 Proceedings of the 2008 Fifth International Conference on Quantitative Evaluation of Systems
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
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 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
Counterexamples for timed probabilistic reachability
FORMATS'05 Proceedings of the Third international conference on Formal Modeling and Analysis of Timed Systems
Extended directed search for probabilistic timed reachability
FORMATS'06 Proceedings of the 4th international conference on Formal Modeling and Analysis of Timed Systems
Fair adversaries and randomization in two-player games
FOSSACS'10 Proceedings of the 13th international conference on Foundations of Software Science and Computational Structures
Defining Fairness in Reactive and Concurrent Systems
Journal of the ACM (JACM)
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
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We propose a way of presenting and computing a counterexample in probabilistic LTL model checking for discrete-time Markov chains. In qualitative probabilistic model checking, we present a counterexample as a pair (*** ,*** ), where *** ,*** are finite words such that all paths that extend *** and have infinitely many occurrences of *** violate the specification. In quantitative probabilistic model checking, we present a counterexample as a pair (W ,R ), where W is a set of such finite words *** and R is a set of such finite words *** . Moreover, we suggest how the counterexample presented helps the user identify the underlying error in the system by means of an interactive game with the model checker.