We present an approach for the verification of feed-forward neural networks in which all nodes have a piece-wise linear activation function. Such networks are often used in deep learning and have been shown to be hard to verify for modern satisfiability modulo theory (SMT) and integer linear programming (ILP) solvers.The starting point of our approach is the addition of a global linear approximation of the overall network behavior to the verification problem that helps with SMT-like reasoning over the network behavior. We present a specialized verification algorithm that employs this approximation in a search process in which it infers additional node phases for the non-linear nodes in the network from partial node phase assignments, similar to unit propagation in classical SAT solving. We also show how to infer additional conflict clauses and safe node fixtures from the results of the analysis steps performed during the search. The resulting approach is evaluated on collision avoidance and handwritten digit recognition case studies.

Abstract. We introduce the reactive synthesis competition (SYNTCOMP), a long-term effort intended to stimulate and guide advances in the design and application of synthesis procedures for reactive systems. The first iteration of SYNTCOMP is based on the controller synthesis problem for finite-state systems and safety specifications. We provide an overview of this problem and existing approaches to solve it, and report on the design and results of the first SYNTCOMP. This includes the definition of the benchmark format, the collection of benchmarks, the rules of the competition, and the five synthesis tools that participated. We present and analyze the results of the competition and draw conclusions on the state of the art. Finally, we give an outlook on future directions of SYNTCOMP.

Reinforcement learning algorithms discover policies that maximize reward, but do not necessarily guarantee safety during learning or execution phases. We introduce a new approach to learn optimal policies while enforcing properties expressed in temporal logic. To this end, given the temporal logic specification that is to be obeyed by the learning system, we propose to synthesize a reactive system called a shield. The shield monitors the actions from the learner and corrects them only if the chosen action causes a violation of the specification. We discuss which requirements a shield must meet to preserve the convergence guarantees of the learner. Finally, we demonstrate the versatility of our approach on several challenging reinforcement learning scenarios.

Synthesis of finite state systems from full linear time temporal logic (LTL) specifications is gaining more and more attention as several recent achievements have significantly improved its practical applicability. Many works in this area are based on the Safraless synthesis approach. Here, the computation is usually performed either in an explicit way or using symbolic data structures other than binary decision diagrams (BDDs). In this paper, we close this gap and consider Safraless synthesis using BDDs as state space representation. The key to this combination is the application of novel optimisation techniques which decrease the number of state bits in such a representation significantly. We evaluate our approach on several practical benchmarks, including a new load balancing case study. Our experiments show an improvement of several orders of magnitude over previous approaches.

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Abstract. We present Unbeast v.0.6, a tool for synthesising finitestate systems from specifications written in linear-time temporal logic (LTL). We combine bounded synthesis, specification splitting and symbolic game solving with binary decision diagrams (BDDs), which allows tackling specifications that previous tools were typically unable to handle. In case of realizability of a given specification, our tool computes a prototype implementation in a fully symbolic way, which is especially beneficial for settings with many input and output bits.

We consider a problem on the synthesis of reactive controllers that optimize some a priori unknown performance criterion while interacting with an uncontrolled environment such that the system satisfies a given temporal logic specification. We decouple the problem into two subproblems. First, we extract a (maximally) permissive strategy for the system, which encodes multiple (possibly all) ways in which the system can react to the adversarial environment and satisfy the specifications. Then, we quantify the a priori unknown performance criterion as a (still unknown) reward function and compute an optimal strategy for the system within the operating envelope allowed by the permissive strategy by using the so-called maximin-Q learning algorithm. We establish both correctness (with respect to the temporal logic specifications) and optimality (with respect to the a priori unknown performance criterion) of this twostep technique for a fragment of temporal logic specifications. For specifications beyond this fragment, correctness can still be preserved, but the learned strategy may be sub-optimal. We present an algorithm to the overall problem, and demonstrate its use and computational requirements on a set of robot motion planning examples.

The increased interest in reactive synthesis over the last decade has led to many improved solutions but also to many new questions. In this paper, we discuss the question of how to deal with assumptions on environment behavior. We present four goals that we think should be met and review several different possibilities that have been proposed. We argue that each of them falls short in at least one aspect.Comment: In Proceedings SYNT 2014, arXiv:1407.493