Section: New Results

Timed, Probabilistic, and Stochastic Extensions

Tools for Probabilistic and Stochastic Systems

Participants : Hubert Garavel, Jean-Philippe Gros, Frédéric Lang, Julie Parreaux, Wendelin Serwe.

Formal models and tools dealing with quantititative aspects (such as time, probabilities, and other continuous physical quantities) have become unavoidable for a proper study and computer-aided verification of functional and non-functional properties of cyberphysical systems. The wealth of such formal models is sometimes referred to as a quantitative “zoo” [39].

The CADP toolbox already implements some of these probabilistic/stochastic models, namely DTMCs and CTMCs (Discrete-Time and Continuous-Time Markov Chains), and IMCs (Interactive Markov Chains) [41]. Our long-term goal is to increase the capability and flexibility of the CADP tools, so as to support other quantitative models more easily.

In 2017, we undertook a systematic review of the existing theoretical models and built a comprehensive list of more than 70 software tools implementing these models [37]. The results of this study have been made widely available as a Web catalog (http://cadp.inria.fr/resources/zoo).

In parallel, we also undertook a systematic review [50] of the benchmarks made available for these tools. We downloaded more than $21000$ files from the web and developed triage scripts to analyze these files and classify them automatically, separating various kinds of automata-based models (e.g., Markov chains, Markov automata, hybrid automata, etc.) from temporal-logic formulas. One finding of this “big data” study is the present lack of diversity, as four tools (PRISM, MRMC, STORM, and SiSAT) provide nearly $60\%$ of the models.

To address this issue, we started investigating the probabilistic and stochastic models of complex industrial systems produced by former PhD students of the VASY and CONVECS teams. We analyzed these models (written in BCG, EXP, LOTOS, LNT, SVL, and/or Makefiles) to separate functional aspects from performance ones, leading to a collection of DTMCs, CTMCs, IMCs, and IPCs (Interactive Probabilistic Chains). We updated these models to ensure compatibility with the latest versions of CADP and C compilers, and we started enhancing EXP.OPEN with new features that simplify the parallel composition of IPCs (see § 6.4.1).

On-the-fly Model Checking for Extended Regular Probabilistic Operators

Participant : Radu Mateescu.

Specifying and verifying quantitative properties of concurrent systems requires expressive and user-friendly property languages combining temporal, data-handling, and quantitative aspects. In collaboration with José Ignacio Requeno (Univ. Zaragoza, Spain), we undertook the quantitative analysis of concurrent systems modeled as PTSs (Probabilistic Transition Systems), whose actions contain data values and probabilities. We proposed a new regular probabilistic operator that extends naturally the Until operators of PCTL (Probabilistic Computation Tree Logic)  [38], by specifying the probability measure of a path characterized by a generalized regular formula involving arbitrary computations on data values. We integrated the regular probabilistic operator into MCL, we devised an associated on-the-fly model checking method based on a combined local resolution of linear and Boolean equation systems, and we implemented the method in a prototype extension of the EVALUATOR model checker.

In 2017, we continued experimenting the extended model checker on further examples of protocols (Bounded Retransmission Protocol, randomized philosophers, self-stabilization) and observed that it exhibits a performance comparable with the explicit-state algorithms of the PRISM model checker (http://www.prismmodelchecker.org/). A paper was submitted to an international journal.