Although deep learning is a very successful AI technology, many concerns have been raised about to what extent the decisions making process of deep neural networks can be trusted. Verifying of properties of neural networks such as adversarial robustness and network equivalence sheds light on the trustiness of such systems. We focus on an important family of deep neural networks, the Binarized Neural Networks (BNNs) that are useful in resourceconstrained environments, like embedded devices. We introduce our portfolio solver that is able to encode BNN properties for SAT, SMT, and MIP solvers and run them in parallel, in a portfolio setting. In the paper we propose all the corresponding encodings of different types of BNN layers as well as BNN properties into SAT, SMT, cardinality constrains, and pseudo-Boolean constraints. Our experimental results demonstrate that our solver is capable of verifying adversarial robustness of medium-sized BNNs in reasonable time and seems to scale for larger BNNs. We also report on experiments on network equivalence with promising results.
Wireless Sensor Networks (WSNs) serve as the basis for Internet of Things applications. A WSN consists of a number of spatially distributed sensor nodes, which cooperatively monitor physical or environmental conditions. In order to ensure the dependability of WSN functionalities, several reliability and security requirements have to be fulfilled. In previous work, we applied OMT (Optimization Modulo Theories) solvers to maximize a WSN's lifetime, i.e., to generate an optimal sleep/wake-up scheduling for the sensor nodes. We discovered that the bottleneck for the underlying SMT (Satisfiability Modulo Theories) solvers was typically to solve satisfiable instances. In this paper, we encode the WSN verification problem as a set of Boolean cardinality constraints, therefore SAT solvers can also be applied as underlying solvers. We have experimented with different SAT solvers and also with different SAT encodings of Boolean cardinality constraints. Based on our experiments, the SAT-based approach is very powerful on satisfiable instances, but quite poor on unsatisfiable ones. In this paper, we apply both SAT and SMT solvers in a portfolio setting. Based on our experiments, the MiniCARD+Z3 setting can be considered to be the most powerful one, which outperforms OMT solvers by 1-2 orders of magnitude.
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