Parametric real-time reasoning
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Theoretical Computer Science
Modeling and verification of randomized distributed real-time systems
Modeling and verification of randomized distributed real-time systems
Automatic verification of real-time systems with discrete probability distributions
Theoretical Computer Science
Probabilistic Model Checking of the IEEE 802.11 Wireless Local Area Network Protocol
PAPM-PROBMIV '02 Proceedings of the Second Joint International Workshop on Process Algebra and Probabilistic Methods, Performance Modeling and Verification
Performance analysis of probabilistic timed automata using digital clocks
Formal Methods in System Design
Parametric probabilistic transition systems for system design and analysis
Formal Aspects of Computing
Symbolic model checking for probabilistic timed automata
Information and Computation
Computing Expected Absorption Times for Parametric Determinate Probabilistic Timed Automata
QEST '08 Proceedings of the 2008 Fifth International Conference on Quantitative Evaluation of Systems
Approximate Parameter Synthesis for Probabilistic Time-Bounded Reachability
RTSS '08 Proceedings of the 2008 Real-Time Systems Symposium
Stochastic Games for Verification of Probabilistic Timed Automata
FORMATS '09 Proceedings of the 7th International Conference on Formal Modeling and Analysis of Timed Systems
Behavioral cartography of timed automata
RP'10 Proceedings of the 4th international conference on Reachability problems
Symbolic and parametric model checking of discrete-time markov chains
ICTAC'04 Proceedings of the First international conference on Theoretical Aspects of Computing
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
Model checking for probabilistic timed automata
Formal Methods in System Design
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Probabilistic timed automata can be used to model systems in which probabilistic and timing behaviour coexist. Verification of probabilistic timed automata models is generally performed with regard to a single reference valuation 驴 0 of the timing parameters. Given such a parameter valuation, we present a method for obtaining automatically a constraint K 0 on timing parameters for which the reachability probabilities (1) remain invariant and (2) are equal to the reachability probabilities for the reference valuation. The method relies on parametric analysis of a non-probabilistic version of the probabilistic timed automata model using the "inverse method". The method presents the following advantages. First, since K 0 corresponds to a dense domain around 驴 0 on which the system behaves uniformly, it gives us a measure of robustness of the system. Second, it allows us to obtain a valuation satisfying K 0 which is as small as possible while preserving reachability probabilities, thus making the probabilistic analysis of the system easier and faster in practice. We provide examples of the application of our technique to models of randomized protocols, and introduce an extension of the method allowing the generation of a "probabilistic cartography" of a system.