Abstract. This paper presents the VerCors approach to verification of concurrent software. It first discusses why verification of concurrent software is important, but also challenging. Then it shows how within the VerCors project we use permission-based separation logic to reason about multithreaded Java programs. We discuss in particular how we use the logic to use different implementations of synchronisers in verification, and how we reason about class invariance properties in a concurrent setting. Further, we also show how the approach is suited to reason about programs using a different concurrency paradigm, namely kernel programs using the Single Instruction Multiple Data paradigm. Concretely, we illustrate how permission-based separation logic is suitable to verify functional correctness properties of OpenCL kernels. All verification techniques discussed in this paper are supported by the VerCors tool set. 1

This text is a general, self contained, and tool independent introduction into the Java Modeling Language, JML. It is a preview of a chapter planned to appear in a book about the KeY approach and tool to the verification of Java software. JML is the dominating starting point of KeY style Java verification. However, this paper does not in any way depend on any tool nor verification methodology. Other chapters in this book talk about the usage of JML in KeY style verification. Here, we only refer to KeY in very few places, without relying on it. This introduction is written for all readers with an interest in formal specification of software in general, and anyone who wants to learn about the JML approach to specification in particular. The authors appreciate any comments or questions that help to improve