An extension of the inverse method to probabilistic timed automata

Abstract

Probabilistic timed automata can be used to model systems in which probabilistic and timing behavior coexist. Verification of probabilistic timed automata models is generally performed with regard to a single reference valuation of the timing parameters. Given such a parameter valuation, we present a method for obtaining automatically a constraint 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 nonprobabilistic version of the probabilistic timed automata model using the "inverse method". Our approach is useful for avoiding repeated executions of probabilistic model checking analyses for the same model with different parameter valuations. We provide examples of the application of our technique to models of randomized protocols.

Parameter Synthesis for Parametric Interval Markov Chains

“…Continuous-time parametric and probabilistic models have also been considered in some very restricted settings [9]. Networks of probabilistic processes where the number of processes is a parameter have also been studied in [4,5], and probabilistic timed automata with parameters in clock constraints and invariants have been studied in [1].…”

“…Given a parametric interval I ∈ Int [0,1] (P ) and a parameter valuation ψ : P → [0, 1], we write ψ(I) for the interval of Int [0,1] obtained by substituting in the endpoints of I each parameter p by the value ψ(p). Constraints on parameter valuations are expressions on parameter variables that restrict their potential values.…”

Behavioral Cartography of Timed Automata

“…We have shown in [4] that the minimum (resp. maximum) probability prob of reaching a given location in A[π] is uniquely determined by the trace set of A * [π].…”

“…Parametric Probabilistic Timed Automata (PPTAs) are an extension of those Probabilistic Timed Automata to the parametric case [4]. In this framework, the discrete actions are distributions of actions.…”

Behavioral Cartography of Timed Automata

“…Moreover, a significant part of the real-valued space outside V 0 is also covered. Those examples, as well as other case studies, can be found on Imitator II's Web page 4 .…”