Digitisation and Full Abstraction for Dense-Time Model Checking

We study the digitisation of dense-time behaviours of timed processes, and show how this leads to exact verification methods for a large class of dense-time specifications. These specifications are all closed under inverse digitisation, a robustness property first introduced by Henzinger, Manna, and Pnueli (on timed traces), and extended here to timed failures, enabling us to consider liveness issues in addition to safety properties. We discuss a corresponding model checking algorithm and show that, in many cases, automated verification of such dense-time specifications can in fact be directly performed on the model checker FDR (a commercial product of Formal Systems (Europe) Ltd.). We illustrate this with a small case study (the railway level crossing problem). Finally, we show that integral—or digitised—behaviours are fully abstract with respect to specifications closed under inverse digitisation, and relate this to the efficiency of our model checking algorithm.