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Model checking meets performance evaluation
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Probabilistic model checking in practice: case studies with PRISM
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Statistical probabilistic model checking with a focus on time-bounded properties
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Uniformization with representatives: comprehensive transient analysis of infinite-state QBDs
SMCtools '06 Proceeding from the 2006 workshop on Tools for solving structured Markov chains
Weighted tree automata and weighted logics
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Backward Bisimulation in Markov Chain Model Checking
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CSL model checking algorithms for QBDs
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Formalization of the Standard Uniform random variable
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Formal analysis techniques for gossiping protocols
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Bisimulation relations for weighted automata
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Specification patterns for probabilistic quality properties
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Model Checking of Infinite State Space Markov Chains by Stochastic Bounds
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Distributed Markovian Bisimulation Reduction aimed at CSL Model Checking
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Electronic Notes in Theoretical Computer Science (ENTCS)
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Survey on Directed Model Checking
Model Checking and Artificial Intelligence
PRISM: probabilistic model checking for performance and reliability analysis
ACM SIGMETRICS Performance Evaluation Review
Delayed Nondeterminism in Continuous-Time Markov Decision Processes
FOSSACS '09 Proceedings of the 12th International Conference on Foundations of Software Science and Computational Structures: Held as Part of the Joint European Conferences on Theory and Practice of Software, ETAPS 2009
Scalable Analysis of Scalable Systems
FASE '09 Proceedings of the 12th International Conference on Fundamental Approaches to Software Engineering: Held as Part of the Joint European Conferences on Theory and Practice of Software, ETAPS 2009
HVC '08 Proceedings of the 4th International Haifa Verification Conference on Hardware and Software: Verification and Testing
CSRL model checking with closed-form bounding distributions
Proceedings of the 3rd International Conference on Performance Evaluation Methodologies and Tools
Terminal Coalgebras for Measure-Polynomial Functors
TAMC '09 Proceedings of the 6th Annual Conference on Theory and Applications of Models of Computation
Probabilistic Analysis of Wireless Systems Using Theorem Proving
Electronic Notes in Theoretical Computer Science (ENTCS)
Weak Stochastic Comparisons for Performability Verification
ASMTA '09 Proceedings of the 16th International Conference on Analytical and Stochastic Modeling Techniques and Applications
Efficient Probabilistic Model Checking on General Purpose Graphics Processors
Proceedings of the 16th International SPIN Workshop on Model Checking Software
Reachability in Stochastic Timed Games
ICALP '09 Proceedings of the 36th Internatilonal Collogquium on Automata, Languages and Programming: Part II
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MarCaSPiS: a Markovian Extension of a Calculus for Services
Electronic Notes in Theoretical Computer Science (ENTCS)
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Proceedings of the the 7th joint meeting of the European software engineering conference and the ACM SIGSOFT symposium on The foundations of software engineering
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AAAI'04 Proceedings of the 19th national conference on Artifical intelligence
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Electronic Notes in Theoretical Computer Science (ENTCS)
Strict Divergence for Probabilistic Timed Automata
CONCUR 2009 Proceedings of the 20th International Conference on Concurrency Theory
The COMPASS Approach: Correctness, Modelling and Performability of Aerospace Systems
SAFECOMP '09 Proceedings of the 28th International Conference on Computer Safety, Reliability, and Security
A Bayesian Approach to Model Checking Biological Systems
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Information Processing Letters
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ATVA '09 Proceedings of the 7th International Symposium on Automated Technology for Verification and Analysis
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ICFEM '09 Proceedings of the 11th International Conference on Formal Engineering Methods: Formal Methods and Software Engineering
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Electronic Notes in Theoretical Computer Science (ENTCS)
Automated Game Analysis via Probabilistic Model Checking: a case study
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ETFA'09 Proceedings of the 14th IEEE international conference on Emerging technologies & factory automation
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ATVA'07 Proceedings of the 5th international conference on Automated technology for verification and analysis
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HVC'07 Proceedings of the 3rd international Haifa verification conference on Hardware and software: verification and testing
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RP'11 Proceedings of the 5th international conference on Reachability problems
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ATVA'11 Proceedings of the 9th international conference on Automated technology for verification and analysis
Formalization of finite-state discrete-time Markov chains in HOL
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PRTS: an approach for model checking probabilistic real-time hierarchical systems
ICFEM'11 Proceedings of the 13th international conference on Formal methods and software engineering
Simulation for interactive markov chains
ICNC'06 Proceedings of the Second international conference on Advances in Natural Computation - Volume Part I
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Extended directed search for probabilistic timed reachability
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ABZ'10 Proceedings of the Second international conference on Abstract State Machines, Alloy, B and Z
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VMCAI'06 Proceedings of the 7th international conference on Verification, Model Checking, and Abstract Interpretation
HASL: an expressive language for statistical verification of stochastic models
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Formal Methods in System Design
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Continuous-time Markov chains (CTMCs) have been widely used to determine system performance and dependability characteristics. Their analysis most often concerns the computation of steady-state and transient-state probabilities. This paper introduces a branching temporal logic for expressing real-time probabilistic properties on CTMCs and presents approximate model checking algorithms for this logic. The logic, an extension of the continuous stochastic logic CSL of Aziz et al., contains a time-bounded until operator to express probabilistic timing properties over paths as well as an operator to express steady-state probabilities. We show that the model checking problem for this logic reduces to a system of linear equations (for unbounded until and the steady-state operator) and a Volterra integral equation system (for time-bounded until). We then show that the problem of model-checking time-bounded until properties can be reduced to the problem of computing transient state probabilities for CTMCs. This allows the verification of probabilistic timing properties by efficient techniques for transient analysis for CTMCs such as uniformization. Finally, we show that a variant of lumping equivalence (bisimulation), a well-known notion for aggregating CTMCs, preserves the validity of all formulas in the logic.