Planning problems can be solved not only by planners, but also by model checkers. While the former yield a plan that requires replanning as soon as any fault occurs, the latter provide a “universal” plan (a.k.a. strategy, policy, or controller) able to make decisions under all circumstances. One of the prohibitive aspects of the latter approach is stemming from this very advantage: since it is defined for all possible states of the system, it is typically so large that it does not fit into small memories of embedded devices. As another consequence of the size, its execution may be slow. In this paper, we provide a solution to this issue by linking the model checkers with decision-tree learners, resulting in decision-tree representations of the synthesized strategies. Not only are they dramatically smaller, but also more explainable and orders-of-magnitude faster to execute than plans with replanning. In addition, we describe a method for model validation and debugging via the model checker and the decision-tree learner in the loop. We illustrate the approach on our case study of a robotic arm for picking items in a real industrial setting.

Abstract Recent advances have shown how decision trees are apt data structures for concisely representing strategies (or controllers) satisfying various objectives. Moreover, they also make the strategy more explainable. The recent tool had provided pipelines with tools supporting strategy synthesis for hybrid systems, such as and . We present , a new version with several fundamentally novel features. Most importantly, the user can now provide domain knowledge to be exploited in the decision tree learning process and can also interactively steer the process based on the dynamically provided information. To this end, we also provide a graphical user interface. It allows for inspection and re-computation of parts of the result, suggesting as well as receiving advice on predicates, and visual simulation of the decision-making process. Besides, we interface model checkers of probabilistic systems, namely and and provide dedicated support for categorical enumeration-type state variables. Consequently, the controllers are more explainable and smaller.

Decision tree learning is a popular classification technique most commonly used in machine learning applications. Recent work has shown that decision trees can be used to represent provably-correct controllers concisely. Compared to representations using lookup tables or binary decision diagrams, decision trees are smaller and more explainable. We present dtControl, an easily extensible tool for representing memoryless controllers as decision trees. We give a comprehensive evaluation of various decision tree learning algorithms applied to 10 case studies arising out of correct-by-construction controller synthesis. These algorithms include two new techniques, one for using arbitrary linear binary classifiers in the decision tree learning, and one novel approach for determinizing controllers during the decision tree construction. In particular the latter turns out to be extremely efficient, yielding decision trees with a single-digit number of decision nodes on 5 of the case studies.

Decision tree learning is a popular classification technique most commonly used in machine learning applications. Recent work has shown that decision trees can be used to represent provably-correct controllers concisely. Compared to representations using lookup tables or binary decision diagrams, decision tree representations are smaller and more explainable. We present dtControl, an easily extensible tool offering a wide variety of algorithms for representing memoryless controllers as decision trees. We highlight that the trees produced by dtControl are often very concise with a single-digit number of decision nodes. This demo is based on our tool paper [1].

Simple stochastic games are turn-based 2½-player games with a reachability objective. The basic question asks whether one player can ensure reaching a given target with at least a given probability. A natural extension is games with a conjunction of such conditions as objective. Despite a plethora of recent results on the analysis of systems with multiple objectives, the decidability of this basic problem remains open. In this paper, we present an algorithm approximating the Pareto frontier of the achievable values to a given precision. Moreover, it is an anytime algorithm, meaning it can be stopped at any time returning the current approximation and its error bound.

Statistical model checking (SMC) is a technique for analysis of probabilistic systems that may be (partially) unknown. We present an SMC algorithm for (unbounded) reachability yielding probably approximately correct (PAC) guarantees on the results. We consider both the setting (i) with no knowledge of the transition function (with the only quantity required a bound on the minimum transition probability) and (ii) with knowledge of the topology of the underlying graph. On the one hand, it is the first algorithm for stochastic games. On the other hand, it is the first practical algorithm even for Markov decision processes. Compared to previous approaches where PAC guarantees require running times longer than the age of universe even for systems with a handful of states, our algorithm often yields reasonably precise results within minutes, not requiring the knowledge of mixing time.