Pranav Ashok

Pranav Ashok, Yuliya Butkova, Holger Hermanns et al.

We provide a framework for speeding up algorithms for time-bounded reachability analysis of continuous-time Markov decision processes. The principle is to find a small, but almost equivalent subsystem of the original system and only analyse the subsystem. Candidates for the subsystem are identified through simulations and iteratively enlarged until runs are represented in the subsystem with high enough probability. The framework is thus dual to that of abstraction refinement. We instantiate the framework in several ways with several traditional algorithms and experimentally confirm orders-of-magnitude speed ups in many cases.

Pranav Ashok, Mathias Jackermeier, Jan Křetínský et al.

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 dtControl had provided pipelines with tools supporting strategy synthesis for hybrid systems, such as SCOTS and Uppaal Stratego. We present dtControl 2.0, 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 Storm and PRISM and provide dedicated support for categorical enumeration-type state variables. Consequently, the controllers are more explainable and smaller.

Pranav Ashok, Vahid Hashemi, Jan Křetínský et al.

While abstraction is a classic tool of verification to scale it up, it is not used very often for verifying neural networks. However, it can help with the still open task of scaling existing algorithms to state-of-the-art network architectures. We introduce an abstraction framework applicable to fully-connected feed-forward neural networks based on clustering of neurons that behave similarly on some inputs. For the particular case of ReLU, we additionally provide error bounds incurred by the abstraction. We show how the abstraction reduces the size of the network, while preserving its accuracy, and how verification results on the abstract network can be transferred back to the original network.

Pranav Ashok, Mathias Jackermeier, Pushpak Jagtap et al.

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.

Pranav Ashok, Jan Křetínský, Maximilian Weininger

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 or the topology of the whole model.

Pranav Ashok, Krishnendu Chatterjee, Przemyslaw Daca et al.

Markov decision processes (MDPs) are standard models for probabilistic systems with non-deterministic behaviours. Long-run average rewards provide a mathematically elegant formalism for expressing long term performance. Value iteration (VI) is one of the simplest and most efficient algorithmic approaches to MDPs with other properties, such as reachability objectives. Unfortunately, a naive extension of VI does not work for MDPs with long-run average rewards, as there is no known stopping criterion. In this work our contributions are threefold. (1) We refute a conjecture related to stopping criteria for MDPs with long-run average rewards. (2) We present two practical algorithms for MDPs with long-run average rewards based on VI. First, we show that a combination of applying VI locally for each maximal end-component (MEC) and VI for reachability objectives can provide approximation guarantees. Second, extending the above approach with a simulation-guided on-demand variant of VI, we present an anytime algorithm that is able to deal with very large models. (3) Finally, we present experimental results showing that our methods significantly outperform the standard approaches on several benchmarks.