Section: New Results

Timed, Probabilistic, and Stochastic Extensions

Participant : Hubert Garavel.

Process calculi provide a suitable formal framework for describing and analyzing concurrent systems, but need to be extended to model refined aspects of these systems. For instance, it may be necessary to represent probabilistic choices (in addition to deterministic and nondeterministic choices) as well as delays and latencies governed by probability laws. Many such extensions have been proposed in the literature, some of which have been implemented in software tools and applied to nontrivial problems. In particular, two of these extensions (namely, Interactive Markov Chains and Interactive Probabilistic Chains) are implemented in CADP. Despite these achievements, the state of the art is not satisfactory as the extended languages primarily focus on the probabilistic and stochastic aspects, leaving away the expressive and user-friendly features that process calculi provide for describing conventional concurrent systems.

In 2012, we undertook a study to merge probabilistic and stochastic aspects into modern high-level languages such as LNT. This work is done at Saarland University under the aegis of the Alexander von Humboldt foundation, in collaboration also with RWTH Aachen and Oxford University. We investigated the theoretical concepts, as well as their integration into modeling languages, together with the corresponding behavioural equivalences and temporal logics.

We also started experimenting with state-of-the-art software implementations, such as MODEST and PASS (Saarland University), COMPASS and MRMC (RWTH Aachen), and PRISM (Oxford University). Two of these tools (namely, MODEST and PRISM) have been used for lab exercises in the Applied Concurrency Theory block course created by H. Garavel at Saarland University. Following these experiments, evaluation reports have been produced, which provide feedback about issues and suggestions for enhancements. These reports have been addressed to the respective authors of each tool and already led to improvements in certain tools.