Durations for Truly-Concurrent Transitions

In this article we take a rather different view on models for real-time systems. First of all, transitions are not instantaneous. They really bear time changes. Secondly, the model is of geometric inspiration (following the ideas of [24]). It is intuitively clearer than other models in that executions can really be pictured as curves (or “trajectories”). Finally it is based on a model of true concurrency which can express scheduling properties (see [12]). We present the model in a very progressive way, starting from ordinary transition systems, then going through some truly concurrent operational models, to end up with a fully formalized model for real-time systems (with an application to a subset of timed CCS). The model (timed higher-dimensional automata or timed HDA in short) is made into a category where morphisms are simulations. It is shown to have many interesting algebraic (complete, co-complete, cartesian closed, monoidal closed) and computer-scientific properties (the timing laws are given naturally by the categorical combinators). A discussion of important matters such as fairness and Zeno is also provided.