  Owing to their remarkable learning capabilities and performance in real-world
applications, the use of machine learning systems based on Neural Networks
(NNs) has been continuously increasing. However, various case studies and
empirical findings in the literature suggest that slight variations to NN
inputs can lead to erroneous and undesirable NN behavior. This has led to
considerable interest in their formal analysis, aiming to provide guarantees
regarding a given NN's behavior. Existing frameworks provide robustness and/or
safety guarantees for the trained NNs, using satisfiability solving and linear
programming. We proposed FANNet, the first model checking-based framework for
analyzing a broader range of NN properties. However, the state-space explosion
associated with model checking entails a scalability problem, making the FANNet
applicable only to small NNs. This work develops state-space reduction and
input segmentation approaches, to improve the scalability and timing efficiency
of formal NN analysis. Compared to the state-of-the-art FANNet, this enables
our new model checking-based framework to reduce the verification's timing
overhead by a factor of up to 8000, making the framework applicable to NNs even
with approximately $80$ times more network parameters. This in turn allows the
analysis of NN safety properties using the new framework, in addition to all
the NN properties already included with FANNet. The framework is shown to be
efficiently able to analyze properties of NNs trained on healthcare datasets as
well as the well--acknowledged ACAS Xu NNs.
