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We consider the problem of explaining the temporal behavior of black-boxsystems using human-interpretable models. To this end, based on recent researchtrends, we rely on the fundamental yet interpretable models of deterministicfinite automata (DFAs) and linear temporal logic (LTL) formulas. In contrast tomost existing works for learning DFAs and LTL formulas, we rely on onlypositive examples. Our motivation is that negative examples are generallydifficult to observe, in particular, from black-box systems. To learnmeaningful models from positive examples only, we design algorithms that relyon conciseness and language minimality of models as regularizers. To this end,our algorithms adopt two approaches: a symbolic and a counterexample-guidedone. While the symbolic approach exploits an efficient encoding of languageminimality as a constraint satisfaction problem, the counterexample-guided onerelies on generating suitable negative examples to prune the search. Both theapproaches provide us with effective algorithms with theoretical guarantees onthe learned models. To assess the effectiveness of our algorithms, we evaluateall of them on synthetic data.

Contains fulltext : 197721.pdf (Author’s version preprint ) (Closed access) Contains fulltext : 197721pub.pdf (Publisher’s version ) (Closed access) Communicating multi-pushdown systems model networks of multi-threaded recursive programs communicating via reliable FIFO channels. We extend the notion of split-width [8] to this setting, improving and simplifying the earlier definition. Split-width, while having the same power of clique-/tree-width, gives a divide-and-conquer technique to prove the bound of a class, thanks to the two basic operations, shuffle and merge, of the split-width algebra. We illustrate this technique on examples. We also obtain simple, uniform and optimal decision procedures for various verification problems parametrised by split-width. Automated Technology for Verification and Analysis: 16th International Symposium, ATVA 2018, Los Angeles, CA, USA, October 7-10, 2018

We study the problem of policy synthesis for uncertain partially observable Markov decision processes (uPOMDPs). The transition probability function of uPOMDPs is only known to belong to a so-called uncertainty set, for instance in the form of probability intervals. Such a model arises when, for example, an agent operates under information limitation due to imperfect knowledge about the accuracy of its sensors. The goal is to compute a policy for the agent that is robust against all possible probability distributions within the uncertainty set. In particular, we are interested in a policy that robustly ensures the satisfaction of temporal logic and expected reward specifications. We state the underlying optimization problem as a semi-infinite quadratically-constrained quadratic program (QCQP), which has finitely many variables and infinitely many constraints. Since QCQPs are non-convex in general and practically infeasible to solve, we resort to the so-called convex-concave procedure to convexify the QCQP. Even though convex, the resulting optimization problem still has infinitely many constraints and is NP-hard. For uncertainty sets that form convex polytopes, we provide a transformation of the problem to a convex QCQP with finitely many constraints. We demonstrate the feasibility of our approach by means of several case studies that highlight typical bottlenecks for our problem. In particular, we show that we are able to solve benchmarks with hundreds of thousands of states, hundreds of different observations, and we investigate the effect of different levels of uncertainty in the models.

Recurrent neural networks (RNNs) have emerged as an effective representation of control policies in sequential decision-making problems. However, a major drawback in the application of RNN-based policies is the difficulty in providing formal guarantees on the satisfaction of behavioral specifications, e.g. safety and/or reachability. By integrating techniques from formal methods and machine learning, we propose an approach to automatically extract a finite-state controller (FSC) from an RNN, which, when composed with a finite-state system model, is amenable to existing formal verification tools. Specifically, we introduce an iterative modification to the so-called quantized bottleneck insertion technique to create an FSC as a randomized policy with memory. For the cases in which the resulting FSC fails to satisfy the specification, verification generates diagnostic information. We utilize this information to either adjust the amount of memory in the extracted FSC or perform focused retraining of the RNN. While generally applicable, we detail the resulting iterative procedure in the context of policy synthesis for partially observable Markov decision processes (POMDPs), which is known to be notoriously hard. The numerical experiments show that the proposed approach outperforms traditional POMDP synthesis methods by 3 orders of magnitude within 2% of optimal benchmark values., 8 pages, 5 figures, 1 table

We study strategy synthesis for partially observable Markov decision processes (POMDPs). The particular problem is to determine strategies that provably adhere to (probabilistic) temporal logic constraints. This problem is computationally intractable and theoretically hard. We propose a novel method that combines techniques from machine learning and formal verification. First, we train a recurrent neural network (RNN) to encode POMDP strategies. The RNN accounts for memory-based decisions without the need to expand the full belief space of a POMDP. Secondly, we restrict the RNN-based strategy to represent a finite-memory strategy and implement it on a specific POMDP. For the resulting finite Markov chain, efficient formal verification techniques provide provable guarantees against temporal logic specifications. If the specification is not satisfied, counterexamples supply diagnostic information. We use this information to improve the strategy by iteratively training the RNN. Numerical experiments show that the proposed method elevates the state of the art in POMDP solving by up to three orders of magnitude in terms of solving times and model sizes.

We study synthesis problems with constraints in partially observable Markov decision processes (POMDPs), where the objective is to compute a strategy for an agent that is guaranteed to satisfy certain safety and performance specifications. Verification and strategy synthesis for POMDPs are, however, computationally intractable in general. We alleviate this difficulty by focusing on planning applications and exploiting typical structural properties of such scenarios; for instance, we assume that the agent has the ability to observe its own position inside an environment. We propose an abstraction refinement framework which turns such a POMDP model into a (fully observable) probabilistic two-player game (PG). For the obtained PGs, efficient verification and synthesis tools allow to determine strategies with optimal safety and performance measures, which approximate optimal schedulers on the POMDP. If the approximation is too coarse to satisfy the given specifications, an refinement scheme improves the computed strategies. As a running example, we use planning problems where an agent moves inside an environment with randomly moving obstacles and restricted observability. We demonstrate that the proposed method advances the state of the art by solving problems several orders-of-magnitude larger than those that can be handled by existing POMDP solvers. Furthermore, this method gives guarantees on safety constraints, which is not supported by the majority of the existing solvers.

We introduce the concept of structured synthesis for Markov decision processes where the structure is induced from finitely many pre-specified options for a system configuration. The resulting synthesis problem is in general a nonlinear programming problem (NLP) with integer variables. As solving NLPs is in general not feasible, we present an alternative approach. We present a transformation of models specified in the {PRISM} probabilistic programming language to models that account for all possible system configurations by means of nondeterministic choices. Together with a control module that ensures consistent configurations throughout the system, this transformation enables the use of optimized tools for model checking in a black-box fashion. While this transformation increases the size of a model, experiments with standard benchmarks show that the method provides a feasible approach for structured synthesis. Moreover, we demonstrate the usefulness along a realistic case study involving surveillance by unmanned aerial vehicles in a shipping facility.

We study planning problems where autonomous agents operate inside environments that are subject to uncertainties and not fully observable. Partially observable Markov decision processes (POMDPs) are a natural formal model to capture such problems. Because of the potentially huge or even infinite belief space in POMDPs, synthesis with safety guarantees is, in general, computationally intractable. We propose an approach that aims to circumvent this difficulty: in scenarios that can be partially or fully simulated in a virtual environment, we actively integrate a human user to control an agent. While the user repeatedly tries to safely guide the agent in the simulation, we collect data from the human input. Via behavior cloning, we translate the data into a strategy for the POMDP. The strategy resolves all nondeterminism and non-observability of the POMDP, resulting in a discrete-time Markov chain (MC). The efficient verification of this MC gives quantitative insights into the quality of the inferred human strategy by proving or disproving given system specifications. For the case that the quality of the strategy is not sufficient, we propose a refinement method using counterexamples presented to the human. Experiments show that by including humans into the POMDP verification loop we improve the state of the art by orders of magnitude in terms of scalability.

We consider turn-based stochastic games whose winning conditions are conjunctions of satisfaction objectives for long-run average rewards, and address the problem of finding a strategy that almost surely maintains the averages above a given multi-dimensional threshold vector. We show that strategies constructed from Pareto set approximations of expected energy objectives are \"-optimal for the corresponding average rewards. We further apply our methods to compositional strategy synthesis for multi-component stochastic games that leverages composition rules for probabilistic automata, which we extend for long-run ratio rewards with fairness. We implement the techniques and illustrate our methods on a case study of automated compositional synthesis of controllers for aircraft primary electric power distribution networks that ensure a given level of reliability.