@article{12738, abstract = {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 controllable and adversarial non-determinism. Lexicographic order allows one to consider multiple objectives with a strict preference order. To the best of our knowledge, stochastic games with lexicographic objectives have not been studied before. For a mixture of reachability and safety objectives, we show that deterministic lexicographically optimal strategies exist 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 the computation of optimal strategies in a sequence of single-objectives games. For omega-regular objectives, we restrict our analysis to one-player games, also known as Markov decision processes. We show that lexicographically optimal 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.}, author = {Chatterjee, Krishnendu and Katoen, Joost P and Mohr, Stefanie and Weininger, Maximilian and Winkler, Tobias}, issn = {1572-8102}, journal = {Formal Methods in System Design}, publisher = {Springer Nature}, title = {{Stochastic games with lexicographic objectives}}, doi = {10.1007/s10703-023-00411-4}, year = {2023}, } @inproceedings{8272, abstract = {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.}, author = {Chatterjee, Krishnendu and Katoen, Joost P and Weininger, Maximilian and Winkler, Tobias}, booktitle = {International Conference on Computer Aided Verification}, isbn = {9783030532901}, issn = {16113349}, pages = {398--420}, publisher = {Springer Nature}, title = {{Stochastic games with lexicographic reachability-safety objectives}}, doi = {10.1007/978-3-030-53291-8_21}, volume = {12225}, year = {2020}, } @inproceedings{79, abstract = {Markov Decision Processes (MDPs) are a popular class of models suitable for solving control decision problems in probabilistic reactive systems. We consider parametric MDPs (pMDPs) that include parameters in some of the transition probabilities to account for stochastic uncertainties of the environment such as noise or input disturbances. We study pMDPs with reachability objectives where the parameter values are unknown and impossible to measure directly during execution, but there is a probability distribution known over the parameter values. We study for the first time computing parameter-independent strategies that are expectation optimal, i.e., optimize the expected reachability probability under the probability distribution over the parameters. We present an encoding of our problem to partially observable MDPs (POMDPs), i.e., a reduction of our problem to computing optimal strategies in POMDPs. We evaluate our method experimentally on several benchmarks: a motivating (repeated) learner model; a series of benchmarks of varying configurations of a robot moving on a grid; and a consensus protocol.}, author = {Arming, Sebastian and Bartocci, Ezio and Chatterjee, Krishnendu and Katoen, Joost P and Sokolova, Ana}, location = {Beijing, China}, pages = {53--70}, publisher = {Springer}, title = {{Parameter-independent strategies for pMDPs via POMDPs}}, doi = {10.1007/978-3-319-99154-2_4}, volume = {11024}, year = {2018}, } @article{10418, abstract = {We present a new proof rule for proving almost-sure termination of probabilistic programs, including those that contain demonic non-determinism. An important question for a probabilistic program is whether the probability mass of all its diverging runs is zero, that is that it terminates "almost surely". Proving that can be hard, and this paper presents a new method for doing so. It applies directly to the program's source code, even if the program contains demonic choice. Like others, we use variant functions (a.k.a. "super-martingales") that are real-valued and decrease randomly on each loop iteration; but our key innovation is that the amount as well as the probability of the decrease are parametric. We prove the soundness of the new rule, indicate where its applicability goes beyond existing rules, and explain its connection to classical results on denumerable (non-demonic) Markov chains.}, author = {Mciver, Annabelle and Morgan, Carroll and Kaminski, Benjamin Lucien and Katoen, Joost P}, issn = {2475-1421}, journal = {Proceedings of the ACM on Programming Languages}, location = {Los Angeles, CA, United States}, number = {POPL}, publisher = {Association for Computing Machinery}, title = {{A new proof rule for almost-sure termination}}, doi = {10.1145/3158121}, volume = {2}, year = {2017}, }