Section: New Results

Timed, Probabilistic, and Stochastic Extensions

Participants : Hubert Garavel, Frédéric Lang, Radu Mateescu.

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 2013, we did the following steps to progress our agenda of bridging the gap between functional verification and quantitative evaluation:

• We equipped CADP with a new tool named BCG_CMP, which enables to compare quantitative models modulo probabilistic and stochastic variants of strong bisimulation and branching bisimulation. Such comparison relations were not available in the BISIMULATOR tool that already existed in CADP.

• We investigated the feasibility of creating interconnections between mainstream verification tools for probabilistic and stochastic systems. In a first step, we focused on the DTMC (Discrete-Time Markov Chain) model and on three mainstream tools: CADP (Grenoble), MRMC (Aachen), and PRISM (Birmingham-Oxford).

  We developed translation tools to perform conversions between the various formats of these tools (“.aut” and “.bcg” for CADP, “.tra/.sta/.lab” for MRMC, “.pm” and “.tra/.sta/.lab” for PRISM). So doing, we reported one bug in MRMC and five minor issues in PRISM. By discussing with Dave Parker (University of Birmingham), we contributed to the introduction in PRISM 4.1 of two new options “-importmodel” and “-exportmodel” that greatly simplify exchanges of models between PRISM and other tools.

  We developed a generator of random DTMCs in CADP, MRMC, and PRISM formats, and undertook the construction of a collection of DTMCs, which we used to compare the performance and scalability of CADP and PRISM.

• We started to investigate the evaluation of temporal logic properties on extended DTMCs, in which transitions are labeled with probabilities and optional actions. For this purpose, we developed a new prototype XTL library (consisting of XTL and C code) encoding the PCTL (Probabilistic CTL) temporal logic  [50] . This new PCTL library enables the specifier to combine data-based, discrete-time, and probabilistic properties of DTMCs in a uniform way.