QEST '05 Proceedings of the Second International Conference on the Quantitative Evaluation of Systems
Principles of Model Checking (Representation and Mind Series)
Principles of Model Checking (Representation and Mind Series)
Probabilistic reachability and safety for controlled discrete time stochastic hybrid systems
Automatica (Journal of IFAC)
Interpolation Processes: Basic Theory and Applications
Interpolation Processes: Basic Theory and Applications
On the connections between PCTL and dynamic programming
Proceedings of the 13th ACM international conference on Hybrid systems: computation and control
Verification of discrete time stochastic hybrid systems: A stochastic reach-avoid decision problem
Automatica (Journal of IFAC)
Quantitative automata model checking of autonomous stochastic hybrid systems
Proceedings of the 14th international conference on Hybrid systems: computation and control
Adaptive Gridding for Abstraction and Verification of Stochastic Hybrid Systems
QEST '11 Proceedings of the 2011 Eighth International Conference on Quantitative Evaluation of SysTems
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
Probabilistic invariance of mixed deterministic-stochastic dynamical systems
Proceedings of the 15th ACM international conference on Hybrid Systems: Computation and Control
Regularization of bellman equations for infinite-horizon probabilistic properties
Proceedings of the 15th ACM international conference on Hybrid Systems: Computation and Control
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This work investigates the approximate verification of probabilistic specifications expressed as any non-nested PCTL formula over Markov processes on general state spaces. The contribution puts forward new algorithms, based on higher-order function approximation, for the efficient computation of approximate solutions with explicit bounds on the error. Approximation error related to higher-order approximations can be substantially lower than those for piece-wise constant (zeroth-order) approximations known in the literature and, unlike the latter, can display convergence in time to a finite value. Furthermore, higher-order approximation procedures, which depend on the partitioning of the state space, can lead to lower partition cardinality than the related piece-wise constant ones. The work is first presented for Markov processes over Euclidean spaces and thereafter extended to hybrid spaces characterizing models known as Stochastic Hybrid Systems.