LNCS

We study turn-based stochastic zero-sum games with lexicographic preferences over reachability and safety objectives. Stochastic games are standard models in control, verification, and synthesis of stochastic reactive systems that exhibit both randomness as well as angelic and demonic non-determinism. Lexicographic order allows to consider multiple objectives with a strict preference order over the satisfaction of the objectives. To the best of our knowledge, stochastic games with lexicographic objectives have not been studied before. We establish determinacy of such games and present strategy and computational complexity results. For strategy complexity, we show that lexicographically optimal strategies exist that are deterministic and memory is only required to remember the already satisfied and violated objectives. For a constant number of objectives, we show that the relevant decision problem is in NP∩coNP , matching the current known bound for single objectives; and in general the decision problem is PSPACE -hard and can be solved in NEXPTIME∩coNEXPTIME . We present an algorithm that computes the lexicographically optimal strategies via a reduction to computation of optimal strategies in a sequence of single-objectives games. We have implemented our algorithm and report experimental results on various case studies

Multi-cost Bounded Reachability in MDP

We provide an efficient algorithm for multi-objective model-checking problems on Markov decision processes (MDPs) with multiple cost structures. The key problem at hand is to check whether there exists a scheduler for a given MDP such that all objectives over cost vectors are fulfilled. Reachability and expected cost objectives are covered and can be mixed. Empirical evaluation shows the algorithm’s scalability. We discuss the need for output beyond Pareto curves and exploit the available information from the algorithm to support decision makers

Artefact containing model checker Storm binary, as presented in the TACAS 2018 paper 'Multi-Cost Bounded Reachability in MDP'

<div>This dataset relates to the paper "Multi-Cost Bounded Reachability in MDP" which aimed to develop an efficient algorithm for multi-objective model checking problems on Markov decision processes (MDPs) with multiple cost structures.</div><div><br></div><div>The dataset includes the Storm model checker binary used to execute examples, and model files and queries. The most recent version of Storm can be found at http://www.stormchecker.org. The virtual machine used with this dataset is available at <a href="https://doi.org/10.6084/m9.figshare.5896615">https://doi.org/10.6084/m9.figshare.5896615</a>. </div><div><br></div><div>Scripts are included in .sh (Unix SHell) format, and the benchmark model files contain .txt, .prism, .props, .py, .nm and .prctl formats. Where models have been taken from openly accessible repositories, this information is included in individual README files. </div><div><br></div><div>A README is also provided which gives installation instructions as well as guidance to checking the algorithm using the models provided, reproducing results of the published paper, and checking other multi-cost bounded properties via their unfolding.</div><div><br></div><div><br></div