Numerical methods for ordinary differential systems: the initial value problem
Numerical methods for ordinary differential systems: the initial value problem
The complexity of probabilistic verification
Journal of the ACM (JACM)
Model-checking continuous-time Markov chains
ACM Transactions on Computational Logic (TOCL)
Theoretical Computer Science - Latin American theoretical informatics
Model-Checking Algorithms for Continuous-Time Markov Chains
IEEE Transactions on Software Engineering
Analysis of Software Fault Removal Policies Using a Non-Homogeneous Continuous Time Markov Chain
Software Quality Control
QEST '05 Proceedings of the Second International Conference on the Quantitative Evaluation of Systems
Computing Battery Lifetime Distributions
DSN '07 Proceedings of the 37th Annual IEEE/IFIP International Conference on Dependable Systems and Networks
Principles of Model Checking (Representation and Mind Series)
Principles of Model Checking (Representation and Mind Series)
Complementation, Disambiguation, and Determinization of Büchi Automata Unified
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part I
Model Checking HML on Piecewise-Constant Inhomogeneous Markov Chains
FORMATS '08 Proceedings of the 6th international conference on Formal Modeling and Analysis of Timed Systems
Quantitative Model Checking of Continuous-Time Markov Chains Against Timed Automata Specifications
LICS '09 Proceedings of the 2009 24th Annual IEEE Symposium on Logic In Computer Science
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
CONCUR'12 Proceedings of the 23rd international conference on Concurrency Theory
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We investigate the problem of verifying linear-time properties against inhomogeneous continuous-time Markov chains (ICTMCs). A fundamental question we address is how to compute reachability probabilities. We consider two variants: time-bounded and unbounded reachability. It turns out that both can be characterized as the least solution of a system of integral equations. We show that for the time-bounded case, the obtained integral equations can be transformed into a system of ordinary differential equations; for the time-unbounded case, we identify two sufficient conditions, namely the eventually periodic assumption and the eventually uniform assumption , under which the problem can be reduced to solving a time-bounded reachability problem for the ICTMCs and a reachability problem for a DTMC. These results provide the basis for a model checking algorithm for LTL. Under the eventually stable assumption , we show how to compute the probability of a set of ICTMC paths which satisfy a given LTL formula. By an automata-based approach, we reduce this problem to the previous established results for reachability problems.