Artificial Neural networks (ANNs) are powerful computing systems employed for various applications due to their versatility to generalize and to respond to unexpected inputs/patterns. However, implementations of ANNs for safetycritical systems might lead to failures, which are hardly predicted in the design phase since ANNs are highly parallel and their parameters are hardly interpretable. Here we develop and evaluate a novel symbolic software verification framework based on incremental bounded model checking (BMC) to check for adversarial cases and coverage methods in multi-layer perceptron (MLP). In particular, we further develop the efficient SMTbased Context-Bounded Model Checker for Graphical Processing Units (ESBMC-GPU) in order to ensure the reliability of certain safety properties in which safety-critical systems can fail and make incorrect decisions, thereby leading to unwanted material damage or even put lives in danger. This paper marks the first symbolic verification framework to reason over ANNs implemented in CUDA. Our experimental results show that our approach implemented in ESBMC-GPU can successfully verify safety properties and covering methods in ANNs and correctly generate 28 adversarial cases in MLPs.

QNNVerifier is the first open-source tool for verifying implementations of neural networks that takes into account the finite word-length (i.e. quantization) of their operands. The novel support for quantization is achieved by employing state-of-the-art software model checking (SMC) techniques. It translates the implementation of neural networks to a decidable fragment of first-order logic based on satisfiability modulo theories (SMT). The effects of fixed-and floatingpoint operations are represented through direct implementations given a hardware-determined precision. Furthermore, QNNVerifier allows to specify bespoke safety properties and verify the resulting model with different verification strategies (incremental and k-induction) and SMT solvers. Finally, QNNVerifier is the first tool that combines invariant inference via interval analysis and discretization of non-linear activation functions to speed up the verification of neural networks by orders of magnitude. A video presentation of QNNVerifier is available at https://youtu.be/7jMgOL41zTY. CCS Concepts:• Computing methodologies → Neural networks; • Software and its engineering → Formal software verification.

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