Equivalence and model checking problems can be encoded into computing fixed points on dependency graphs. Dependency graphs represent causal dependencies among the nodes of the graph by means of hyper-edges. We suggest to extend the model of dependency graphs with so-called negation edges in order t o increase their applicability. The graphs (as well as the verification problems) suffer from the state space explosion problem. To combat this issue, we design an on-the-fly algorithm for efficiently computing fixed points on extended dependency graphs. Our algorithm supplements previous approaches with the possibility to back-propagate, in certain scenarios, the domain value 0, in addition to the standard back-propagation of the value 1. Finally, we design a distributed version of the algorithm, implement it in our open-source tool TAPAAL, and demonstrate the efficiency of our general approach on the benchmark of Petri net models and CTL queries from the annual Model Checking Contest.

Summary This paper presents the motivation for and outcomes of an engineering research project on certifiable Java for embedded systems. The project supports the upcoming standard for safety‐critical Java, which defines a subset of Java and libraries aiming for development of high criticality systems. The outcome of this project include prototype safety‐critical Java implementations, a time‐predictable Java processor, analysis tools for memory safety, and example applications to explore the usability of safety‐critical Java for this application area. The text summarizes developments and key contributions and concludes with the lessons learned. Copyright © 2016 John Wiley & Sons, Ltd.