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)
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)
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
Higher-Order approximations for verification of stochastic hybrid systems
ATVA'12 Proceedings of the 10th international conference on Automated Technology for Verification and Analysis
Formula-free finite abstractions for linear temporal verification of stochastic hybrid systems
Proceedings of the 16th international conference on Hybrid systems: computation and control
Quantitative automata-based controller synthesis for non-autonomous stochastic hybrid systems
Proceedings of the 16th international conference on Hybrid systems: computation and control
Rewarding probabilistic hybrid automata
Proceedings of the 16th international conference on Hybrid systems: computation and control
Characterization and computation of infinite-horizon specifications over Markov processes
Theoretical Computer Science
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This work studies Bellman integral equations arising in infinite-horizon probabilistic verification problems for discrete time homogeneous Markov processes over general state spaces. The problems of interest are expressed via specifications such as probabilistic reachability, invariance, reach-avoid and mean exit time. The contribution shows that the uniqueness of the solutions of the corresponding Bellman equations depends on the presence of absorbing sets within the state space. Furthermore, the work puts forward methods to modify the integral equations to obtain unique solutions for them, techniques to compute such solutions with explicit bounds on the approximation error, and conditions to characterize the possible presence of absorbing sets over the state space.