We present automatic verification techniques for the modelling and analysis of probabilistic
systems that incorporate competitive behaviour. These systems are modelled as turn-based …

This chapter presents that part of the theory of the μ μ-calculus that is relevant to the model-
checking problem as broadly understood. The μ μ-calculus is one of the most important …

PRISM-games is a tool for modelling, verification and strategy synthesis for stochastic multi-
player games. These allow models to incorporate both probability, to represent uncertainty …

Automated verification techniques for stochastic games allow formal reasoning about
systems that feature competitive or collaborative behaviour among rational agents in …

Markov decision processes (MDPs) are standard models for probabilistic systems with non-
deterministic behaviours. Long-run average rewards provide a mathematically elegant …

We propose novel controller synthesis techniques for probabilistic systems modelled using
stochastic two-player games: one player acts as a controller, the second represents its …

Stochastic games are a convenient formalism for modelling systems that comprise rational
agents competing or collaborating within uncertain environments. Probabilistic model …

Desharnais, Gupta, Jagadeesan and Panangaden introduced a family of behavioural
pseudometrics for probabilistic transition systems. These pseudometrics are a quantitative …

Markov decision processes (MDP) and continuous-time MDP (CTMDP) are the fundamental
models for non-deterministic systems with probabilistic uncertainty. Mean payoff (aka long …

We present automatic verification techniques for concurrent stochastic multi-player games
(CSGs) with rewards. To express properties of such models, we adapt the temporal logic …