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The print edition can be ordered at https://www.iospress.nl/book/handbook-of-satisfiability-2/ The published electronic chapters (Version of Record) are available at https://ebooks.iospress.nl/ISBN/978-1-64368-161-0/

Deep neural networks are revolutionizing the way complex systems are designed. Consequently, there is a pressing need for tools and techniques for network analysis and certification. To help in addressing that need, we present Marabou, a framework for verifying deep neural networks. Marabou is an SMT-based tool that can answer queries about a network's properties by transforming these queries into constraint satisfaction problems. It can accommodate networks with different activation functions and topologies, and it performs high-level reasoning on the network that can curtail the search space and improve performance. It also supports parallel execution to further enhance scalability. Marabou accepts multiple input formats, including protocol buffer files generated by the popular TensorFlow framework for neural networks. We describe the system architecture and main components, evaluate the technique and discuss ongoing work.

CVC4 is the latest version of the Cooperating Validity Checker. A joint project of NYU and U Iowa, CVC4 aims to support the useful feature set of CVC3 and SMT-LIBv2 while optimizing the design of the core system architecture and decision procedures to take advantage of recent engineering and algorithmic advances. CVC4 represents a completely new code base; it is a from-scratch rewrite of CVC3, and many subsystems have been completely redesigned. Additional decision procedures for CVC4 are currently under development, but for what it currently achieves, it is a lighter-weight and higher-performing tool than CVC3. We describe the system architecture, subsystems of note, and discuss some applications and continuing work.

Deep neural networks are widely used for nonlinear function approximation with applications ranging from computer vision to control. Although these networks involve the composition of simple arithmetic operations, it can be very challenging to verify whether a particular network satisfies certain input-output properties. This article surveys methods that have emerged recently for soundly verifying such properties. These methods borrow insights from reachability analysis, optimization, and search. We discuss fundamental differences and connections between existing algorithms. In addition, we provide pedagogical implementations of existing methods and compare them on a set of benchmark problems. PreliminariesThis section introduces additional notation and operations that will be used in different verification algorithms to be discussed in the following sections. 8 Section 4.1 discusses interval 8 First-time readers may skip this section and refer back when going into the details of the algorithms. arithmetic to compute node-wise bounds given an input set. Such node-wise bounds are needed in many methods, such as MIPVerify, Duality, ConvDual, Planet, and Reluplex. Section 4.2 discusses interval refinement, which is used in ReluVal and BaB. Section 4.3 discusses methods