Abstract. We present a tool for the formal verification of ANSI-C programs using Bounded Model Checking (BMC). The emphasis is on usability: the tool supports almost all ANSI-C language features, including pointer constructs, dynamic memory allocation, recursion, and the float and double data types. From the perspective of the user, the verification is highly automated: the only input required is the BMC bound. The tool is integrated into a graphical user interface. This is essential for presenting long counterexample traces: the tool allows stepping through the trace in the same way a debugger allows stepping through a program.

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Abstract. This paper presents a model checking tool, SatAbs, that implements a predicate abstraction refinement loop. Existing software verification tools such as Slam, Blast, or Magic use decision procedures for abstraction and simulation that are limited to integers. SatAbs overcomes these limitations by using a SAT-solver. This allows the model checker to handle the semantics of the ANSI-C standard accurately. This includes a sound treatment of bit-vector overflow, and of the ANSI-C pointer arithmetic constructs.

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Abstract. We present a new decision procedure for finite-precision bitvector arithmetic with arbitrary bit-vector operations. Our procedure alternates between generating under-and over-approximations of the original bit-vector formula. An under-approximation is obtained by a translation to propositional logic in which some bit-vector variables are encoded with fewer Boolean variables than their width. If the underapproximation is unsatisfiable, we use the unsatisfiable core to derive an over-approximation based on the subset of predicates that participated in the proof of unsatisfiability. If this over-approximation is satisfiable, the satisfying assignment guides the refinement of the previous underapproximation by increasing, for some bit-vector variables, the number of Boolean variables that encode them. We present experimental results that suggest that this abstraction-based approach can be considerably more efficient than directly invoking the SAT solver on the original formula as well as other competing decision procedures.

Reinforcement Learning (RL) has emerged as an efficient method of choice for solving complex sequential decision making problems in automatic control, computer science, economics, and biology. In this paper we present a model-free RL algorithm to synthesize control policies that maximize the probability of satisfying high-level control objectives given as Linear Temporal Logic (LTL) formulas. Uncertainty is considered in the workspace properties, the structure of the workspace, and the agent actions, giving rise to a Probabilistically-Labeled Markov Decision Process (PL-MDP) with unknown graph structure and stochastic behaviour, which is even more general case than a fully unknown MDP. We first translate the LTL specification into a Limit Deterministic Büchi Automaton (LDBA), which is then used in an on-the-fly product with the PL-MDP. Thereafter, we define a synchronous reward function based on the acceptance condition of the LDBA. Finally, we show that the RL algorithm delivers a policy that maximizes the satisfaction probability asymptotically. We provide experimental results that showcase the efficiency of the proposed method.

Deployment of deep neural networks (DNNs) in safety-or security-critical systems requires provable guarantees on their correct behaviour. A common requirement is robustness to adversarial perturbations in a neighbourhood around an input. In this paper we focus on the L0 norm and aim to compute, for a trained DNN and an input, the maximal radius of a safe norm ball around the input within which there are no adversarial examples. Then we define global robustness as an expectation of the maximal safe radius over a test data set. We first show that the problem is NP-hard, and then propose an approximate approach to iteratively compute lower and upper bounds on the network's robustness. The approach is anytime, i.e., it returns intermediate bounds and robustness estimates that are gradually, but strictly, improved as the computation proceeds; tensor-based, i.e., the computation is conducted over a set of inputs simultaneously, instead of one by one, to enable efficient GPU computation; and has provable guarantees, i.e., both the bounds and the robustness estimates can converge to their optimal values. Finally, we demonstrate the utility of the proposed approach in practice to compute tight bounds by applying and adapting the anytime algorithm to a set of challenging problems, including global robustness evaluation, competitive L0 attacks, test case generation for DNNs, and local robustness evaluation on large-scale ImageNet DNNs. We release the code of all case studies via GitHub 1 . 1 The code is available in https://github.com/TrustAI/L0-TRE arXiv:1804.05805v2 [cs.LG] 20 Nov 2018Safety certification for DNNs is challenging owing to the black-box nature of DNNs and the lack of rigorous foundations. An important low-level requirement for DNNs is the robustness to input perturbations. DNNs have been shown to suffer from poor robustness because of their susceptibility to adversarial examples [29]. These are small modifications to an input, sometimes imperceptible to humans, that make the network unstable. As a result, significant effort has been directed towards approaches for crafting adversarial examples or defending against them [2,5,18]. However, the cited approaches provide no formal guarantees, i.e., no conclusion can be made whether adversarial examples remain or how close crafted adversarial examples are to the optimal ones.Recent efforts in the area of automated verification [8,9] have instead focused on methods that generate adversarial examples, if they exist, and provide rigorous robustness proofs otherwise. These techniques rely on either a layer-by-layer exhaustive search of the neighbourhood of an image [8], or a reduction to a constraint solving problem by encoding the network as a set of constraints [9]. Constraint-based approaches are limited to small networks. Exhaustive search, on the other hand, applies to large networks but suffers from the state-space explosion problem. To mitigate this, a Monte-Carlo tree search has been employed [31]. Moreover, a game-based approximate verification approach that...

Abstract. SAT based Bounded Model Checking (BMC) is an efficient method for detecting logical errors in finite-state transition systems. Given a transition system, an LTL property, and a user defined bound k, a bounded model checker generates a propositional formula that is satisfiable if and only if a counterexample to the property of length up to k exists. Standard SAT checkers can be used to check this formula. BMC is complete if k is larger than some pre-computed threshold. It is still unknown how to compute this threshold for general properties. We show that the longest initialized loop-free path in the state graph, also known as the recurrence diameter, is sufficient for Fp properties. The recurrence diameter is also a known over-approximation for the threshold of simple safety properties (Gp). We discuss various techniques to compute the recurrence diameter efficiently and provide experimental results that demonstrate the benefits of using the new approach.