Model-Checking Algorithms for Continuous-Time Markov Chains
IEEE Transactions on Software Engineering
Model Checking Markov Chains with Actions and State Labels
IEEE Transactions on Software Engineering
Model Checking Timed and Stochastic Properties with CSL^{TA}
IEEE Transactions on Software Engineering
Performance evaluation and model checking join forces
Communications of the ACM
Stochastic real-time games with qualitative timed automata objectives
CONCUR'10 Proceedings of the 21st international conference on Concurrency theory
Measuring performance of continuous-time stochastic processes using timed automata
Proceedings of the 14th international conference on Hybrid systems: computation and control
Efficient CTMC model checking of linear real-time objectives
TACAS'11/ETAPS'11 Proceedings of the 17th international conference on Tools and algorithms for the construction and analysis of systems: part of the joint European conferences on theory and practice of software
Automata-based CSL model checking
ICALP'11 Proceedings of the 38th international conference on Automata, languages and programming - Volume Part II
Time-bounded verification of CTMCs against real-time specifications
FORMATS'11 Proceedings of the 9th international conference on Formal modeling and analysis of timed systems
Playing optimally on timed automata with random delays
FORMATS'12 Proceedings of the 10th international conference on Formal Modeling and Analysis of Timed Systems
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We consider the problem of approximating the probability mass of the set of timed paths under a continuous-time Markov chain (CTMC) that are accepted by a deterministic timed automaton (DTA). As opposed to several existing works on this topic, we consider DTA with multiple clocks. Our key contribution is an algorithm to approximate these probabilities using finite difference methods. An error bound is provided which indicates the approximation error. The stepping stones towards this result include rigorous proofs for the measurability of the set of accepted paths and the integral-equation system characterizing the acceptance probability, and a differential characterization for the acceptance probability.