Abstract Abstract interpretation has been shown to be a promising technique for the thread-modular verification of concurrent programs. Central to this is the generation of interferences, in the form of rely-guarantee conditions, conforming to a user-chosen structure. In this work, we introduce one such structure called the conditional-writes domain, designed for programs where it suffices to establish only the conditions under which particular variables are written to by each thread. We formalise our analysis within a novel abstract interpretation framework that is highly modular and can be easily extended to capture other structures for rely-guarantee conditions. We formalise two versions of our approach and evaluate their implementations on a simple programming language.

Abstract Neural networks are often susceptible to minor perturbations in input that cause them to misclassify. A recent solution to this problem is the use of globally-robust neural networks, which employ a function to certify that the classification of an input cannot be altered by such a perturbation. Outputs that pass this test are called certified robust . However, to the authors’ knowledge, these certification functions have not yet been verified at the implementation level. We demonstrate how previous unverified implementations are exploitably unsound in certain circumstances. Moreover, they often rely on approximation-based algorithms, such as power iteration, that (perhaps surprisingly) do not guarantee soundness. To provide assurance that a given output is robust, we implemented and formally verified a certification function for globally-robust neural networks in Dafny. We describe the program, its specifications, and the important design decisions taken for its implementation and verification, as well as our experience applying it in practice.