Analysis of Non-Linear Probabilistic Hybrid Systems

This paper shows how to compute, for probabilistic hybrid systems, the clock approximation and linear phase-portrait approximation that have been proposed for non probabilistic processes by Henzinger et al. The techniques permit to define a rectangular probabilistic process from a non rectangular one, hence allowing the model-checking of any class of systems. Clock approximation, which applies under some restrictions, aims at replacing a non rectangular variable by a clock variable. Linear phase-approximation applies without restriction and yields an approximation that simulates the original process. The conditions that we need for probabilistic processes are the same as those for the classic case.Comment: In Proceedings QAPL 2011, arXiv:1107.074

Exact and Approximate Abstraction for Classes of Stochastic Hybrid Systems

A stochastic hybrid system contains a collection of interacting discrete and continuous components, subject to random behaviour. The formal verification of a stochastic hybrid system often comprises a method for the generation of a finite-state probabilistic system which either represents exactly the behaviour of the stochastic hybrid system, or which approximates conservatively its behaviour. We extend such abstraction-based formal verification of stochastic hybrid systems in two ways. Firstly, we generalise previous results by showing how bisimulation-based abstractions of non-probabilistic hybrid automata can be lifted to the setting of probabilistic hybrid automata, a subclass of stochastic hybrid systems in which probabilistic choices can be made with respect to finite, discrete alternatives only. Secondly, we consider the problem of obtaining approximate abstractions for discrete-time stochastic systems in which there are continuous probabilistic choices with regard to the slopes of certain system variables. We restrict our attention to the subclass of such systems in which the approximate abstraction of such a system, obtained using the previously developed techniques of Fraenzle et al., results in a probabilistic rectangular hybrid automaton, from which in turn a finite-state probabilistic system can be obtained. We illustrate this technique with an example, using the probabilistic model checking tool PRISM

A Survey on Continuous Time Computations

We provide an overview of theories of continuous time computation. These theories allow us to understand both the hardness of questions related to continuous time dynamical systems and the computational power of continuous time analog models. We survey the existing models, summarizing results, and point to relevant references in the literature

IMITATOR II: A Tool for Solving the Good Parameters Problem in Timed Automata

We present here Imitator II, a new version of Imitator, a tool implementing the "inverse method" for parametric timed automata: given a reference valuation of the parameters, it synthesizes a constraint such that, for any valuation satisfying this constraint, the system behaves the same as under the reference valuation in terms of traces, i.e., alternating sequences of locations and actions. Imitator II also implements the "behavioral cartography algorithm", allowing us to solve the following good parameters problem: find a set of valuations within a given bounded parametric domain for which the system behaves well. We present new features and optimizations of the tool, and give results of applications to various examples of asynchronous circuits and communication protocols.Comment: In Proceedings INFINITY 2010, arXiv:1010.611

Maximizing Reachability Probabilities in Rectangular Automata with Random Clocks

This paper proposes an algorithm to maximize reachability probabilities for rectangular automata with random clocks via a history-dependent prophetic scheduler. This model class incorporates time-induced nondeterminism on discrete behavior and nondeterminism in the dynamic behavior. After computing reachable state sets via a forward flowpipe construction, we use backward refinement to compute maximum reachability probabilities. The feasibility of the presented approach is illustrated on a scalable model