Models for Experiments on MDPs for "Stochastic Games with Lexicographic Objectives"
Creators: name: Chatterjee, Krishnendu
name: Katoen, Joost-Pieter
name: Mohr, Stefanie
name: Weiniger, Maximilian
name: Winkler, Tobias
Publisher: name: Zenodo
Year: 2022

description: <strong>Additional Artifact of "Stochastic Games with Lexicographic Objectives" for Section 5.2</strong><br> Authors: Krishnendu Chatterjee, Joost-Pieter Katoen, Stefanie Mohr, Maximilian Weininger, Tobias Winkler<br> This artifact contains the models, run-scripts, and logs to reproduce the results from Section 5.2 "MDP with Lexicographic LTL". The artifact for Section 5.1 can be found here: Stochastic Games with Lexicographic Reachability-Safety Objectives (Artifact of CAV2020 Paper) <em>Abstract of the Paper</em> We study turn-based stochastic zero-sum games with lexicographic preferences over 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. Firstly, for a mixture of reachability and safety objectives, we establish determinacy 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 $\np \cap \conp$, matching the current known bound for single objectives; and in general the decision problem is $\pspace$-hard and can be solved in $\nexptime \cap \conexptime$. 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.<br> Secondly, for omega-regular objectives, we restrict our analysis to one-player games, also known as Markov decision processes, and provide strategy and computational complexity results: for strategy complexity, we show that optimal lexicographic strategies exist and need either randomization or finite memory. We present an algorithm that solves the relevant decision problem in polynomial time. We have implemented our algorithms and report experimental results on various case studies. <em>Installation Instructions</em><br> Two tools are necessary to reproduce the results:<br> * Mungojerrie (https://plv.colorado.edu/wwwmungojerrie/), version 1.1.1 <br> * Storm (https://github.com/moves-rwth/storm), version 1.7.0 <br> Please refer to the original installation instructions of the respective tools. <em><strong>Artifact Structure</strong></em><br> There are two scripts that would reproduce all the results, one for Mungojerrie (run_mungojerrie.sh), and one for Storm (run_storm.sh). Make sure that the executables can be found by adapting the PATH-variable.<br> Otherwise you can try to run the experiments by adapting the scripts accordingly.<br> They can then be started with `./run_storm.sh` and `./run_mungojerrie.sh`. Additionally, there is the folder 'examples', which contains all the models that we used for the experiments and the properties. The models are in the prism-format. The properties for Storm are also in prism-property-format. the properties for Mungojerrie are automata in the hoa-format. Lastly, the folder 'logs' contains the logs that we generated by running the scripts.<br>