Parameter-Independent Strategies for pMDPs via POMDPs

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.Comment: Extended version of a QEST 2018 pape

PrIC3: Property Directed Reachability for MDPs

IC3 has been a leap forward in symbolic model checking. This paper proposes PrIC3 (pronounced pricy-three), a conservative extension of IC3 to symbolic model checking of MDPs. Our main focus is to develop the theory underlying PrIC3. Alongside, we present a first implementation of PrIC3 including the key ingredients from IC3 such as generalization, repushing, and propagation

Accelerated Model Checking of Parametric Markov Chains

Parametric Markov chains occur quite naturally in various applications: they can be used for a conservative analysis of probabilistic systems (no matter how the parameter is chosen, the system works to specification); they can be used to find optimal settings for a parameter; they can be used to visualise the influence of system parameters; and they can be used to make it easy to adjust the analysis for the case that parameters change. Unfortunately, these advancements come at a cost: parametric model checking is---or rather was---often slow. To make the analysis of parametric Markov models scale, we need three ingredients: clever algorithms, the right data structure, and good engineering. Clever algorithms are often the main (or sole) selling point; and we face the trouble that this paper focuses on -- the latter ingredients to efficient model checking. Consequently, our easiest claim to fame is in the speed-up we have often realised when comparing to the state of the art

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

More Scalable LTL Model Checking via Discovering Design-Space Dependencies (D3)

Modern system design often requires comparing several models over a large design space. Different models arise out of a need to weigh different design choices, to check core capabilities of versions with varying features, or to analyze a future version against previous ones. Model checking can compare different models; however, applying model checking off-the-shelf may not scale due to the large size of the design space for today’s complex systems. We exploit relationships between different models of the same (or related) systems to optimize the model-checking search. Our algorithm, D3 , preprocesses the design space and checks fewer model-checking instances, e.g., using nuXmv. It automatically prunes the search space by reducing both the number of models to check, and the number of LTL properties that need to be checked for each model in order to provide the complete model-checking verdict for every individual model-property pair. We formalize heuristics that improve the performance of D3 . We demonstrate the scalability of D3 by extensive experimental evaluation, e.g., by checking 1,620 real-life models for NASA’s NextGen air traffic control system. Compared to checking each model-property pair individually, D3 is up to 9.4 × faster

LNCS

Discrete-time Markov Chains (MCs) and Markov Decision Processes (MDPs) are two standard formalisms in system analysis. Their main associated quantitative objectives are hitting probabilities, discounted sum, and mean payoff. Although there are many techniques for computing these objectives in general MCs/MDPs, they have not been thoroughly studied in terms of parameterized algorithms, particularly when treewidth is used as the parameter. This is in sharp contrast to qualitative objectives for MCs, MDPs and graph games, for which treewidth-based algorithms yield significant complexity improvements. In this work, we show that treewidth can also be used to obtain faster algorithms for the quantitative problems. For an MC with n states and m transitions, we show that each of the classical quantitative objectives can be computed in O((n+m)⋅t2) time, given a tree decomposition of the MC with width t. Our results also imply a bound of O(κ⋅(n+m)⋅t2) for each objective on MDPs, where κ is the number of strategy-iteration refinements required for the given input and objective. Finally, we make an experimental evaluation of our new algorithms on low-treewidth MCs and MDPs obtained from the DaCapo benchmark suite. Our experiments show that on low-treewidth MCs and MDPs, our algorithms outperform existing well-established methods by one or more orders of magnitude

A Practitioner's Guide to MDP Model Checking Algorithms (Artefact)

This artefact allows to review and replicate the experiments from the TACAS'23 paperA Practitioner's Guide to MDP Model Checking Algorithms. The package contains all original logfiles and the scripts that extract the relevant data from those logs to generate the plots as in the paper. Furthermore, the artefact contains the model checking tools `Storm` and `mcsta` with their dependencies and convenient installation scripts as well as all benchmark instances. We provide installation instructions for those LP solvers that, due to licensing reasons, could not be included in this artefact. The user can thus replicate all experiments from the paper. An appropriate subset of the experiments is given to allow a review in a timely manner. In addition, single experiments can be handpicked for replication. Copyright: Open Acces