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Abstract. This chapter is to provide a tutorial and pointers to results and related work on timed automata with a focus on semantical and algorithmic aspects of verification tools. We present the concrete and abstract semantics of timed automata (based on transition rules, regions and zones), decision problems, and algorithms for verification. A detailed description on DBM (Difference Bound Matrices) is included, which is the central data structure behind several verification tools for timed systems. As an example, we give a brief introduction to the tool UPPAAL.

Abstract. Uppaal is a tool suite for automatic verification of safety and bounded liveness properties of real-time systems modeled as networks of timed automata. It includes: a graphical interface that supports graphical and textual representations of networks of timed automata, and automatic transformation from graphical representations to textual format, a compiler that transforms a certain class of linear hybrid systems to networks of timed automata, and a model-checker which is implemented based on constraint-solving techniques. Uppaal also supports diagnostic model-checking providing diagnostic information in case verification of a particular real-time systems fails. The current version of Uppaal is available on the World Wide Web via the Uppaal home page

Recently, there have been several promising techniques developed for schedulability analysis and response time analysis for multiprocessor systems based on over-approximation. This paper contains two contributions. First, to improve the analysis precision, we apply Baruah's window analysis framework [6] to response time analysis for sporadic tasks on multiprocessor systems where the deadlines of tasks are within their periods. The crucial observation is that for global fixed priority scheduling, a response time bound of each task can be efficiently estimated by fixed-point computation without enumerating all the busy window sizes as in [6] for schedulability analysis. The technique is proven to dominate theoretically state-of-the-art techniques for response time analysis for multiprocessor systems. Our experiments also show that the technique results in significant performance improvement compared with several existing techniques for multiprocessor schedulability analysis. As the second main contribution of this paper, we extend the proposed technique to task systems with arbitrary deadlines, allowing tasks to have deadlines beyond the end of their periods. This is a non-trivial extension even for single-processor systems. To our best knowledge, this is the first work for multiprocessor systems in this setting, which involves sophisticated techniques for the characterization and computation of response time bounds.