Accelerating Parametric Probabilistic Verification

We present a novel method for computing reachability probabilities of parametric discrete-time Markov chains whose transition probabilities are fractions of polynomials over a set of parameters. Our algorithm is based on two key ingredients: a graph decomposition into strongly connected subgraphs combined with a novel factorization strategy for polynomials. Experimental evaluations show that these approaches can lead to a speed-up of up to several orders of magnitude in comparison to existing approache

Approximate probabilistic verification of hybrid systems

Hybrid systems whose mode dynamics are governed by non-linear ordinary differential equations (ODEs) are often a natural model for biological processes. However such models are difficult to analyze. To address this, we develop a probabilistic analysis method by approximating the mode transitions as stochastic events. We assume that the probability of making a mode transition is proportional to the measure of the set of pairs of time points and value states at which the mode transition is enabled. To ensure a sound mathematical basis, we impose a natural continuity property on the non-linear ODEs. We also assume that the states of the system are observed at discrete time points but that the mode transitions may take place at any time between two successive discrete time points. This leads to a discrete time Markov chain as a probabilistic approximation of the hybrid system. We then show that for BLTL (bounded linear time temporal logic) specifications the hybrid system meets a specification iff its Markov chain approximation meets the same specification with probability $1$. Based on this, we formulate a sequential hypothesis testing procedure for verifying -approximately- that the Markov chain meets a BLTL specification with high probability. Our case studies on cardiac cell dynamics and the circadian rhythm indicate that our scheme can be applied in a number of realistic settings

Undecidability of model-checking branching-time properties of stateless probabilistic pushdown process

In this paper, we settle a problem in probabilistic verification of infinite--state process (specifically, {\it probabilistic pushdown process}). We show that model checking {\it stateless probabilistic pushdown process} (pBPA) against {\it probabilistic computational tree logic} (PCTL) is undecidable.Comment: Author's comments on referee's report added, Interestin

Probabilistic Verification in Mechanism Design

We introduce a model of probabilistic verification in a mechanism design setting. The principal verifies the agent's claims with statistical tests. The agent's probability of passing each test depends on his type. In our framework, the revelation principle holds. We characterize whether each type has an associated test that best screens out all the other types. In that case, the testing technology can be represented in a tractable reduced form. In a quasilinear environment, we solve for the revenue-maximizing mechanism by introducing a new expression for the virtual value that encodes the effect of testing

A control problem with fuel constraint and Dawson-Watanabe superprocesses

We solve a class of control problems with fuel constraint by means of the log-Laplace transforms of $J$-functionals of Dawson-Watanabe superprocesses. This solution is related to the superprocess solution of quasilinear parabolic PDEs with singular terminal condition. For the probabilistic verification proof, we develop sharp bounds on the blow-up behavior of log-Laplace functionals of $J$-functionals, which might be of independent interest.Comment: Published in at http://dx.doi.org/10.1214/12-AAP908 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org