Section: New Results

Timed, Probabilistic, and Stochastic Extensions

Tools for Probabilistic and Stochastic Systems

Participants : Hubert Garavel, Frédéric Lang.

Formal models and tools dealing with quantitative 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 cyber-physical systems. The wealth of such formal models is sometimes referred to as a quantitative “zoo” [48].

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) [50]. 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 2018, BCG_STEADY and BCG_TRANSIENT were enhanced along the following lines:

  • They were extended to handle single-state Markov chains and to properly compute state solution vectors and transition throughputs on such models.

  • Their command-line options were simplified and warnings are emitted when the input Markov chain contains no stochastic transition.

  • A problem which caused correct Markov chains to be rejected was corrected. This problem was due to floating point conversion and rounding errors.

  • A confusion between state numbers and matrix indices was fixed in the output and error messages.

  • Models containing probabilistic self-loops are now rejected, as was already the case of longer circuits of probabilistic transitions, as both represent similar “timelock” situations.

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[47], 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 2018, we continued improving and using the extended model checker as follows:

  • The model checker now determinizes the dataless regular formulas contained in regular probabilistic operators, ensuring automatically that the linear equation systems produced by the verification of these operators have a unique solution.

  • For nondeterministic data-handling regular formulas contained in regular probabilistic operators, the model checker now produces a warning message informing the user that the determinization has to be done manually.

  • We carried out further experiments to analyze the quantitative behaviour of the Bounded Retransmission Protocol, namely the variation of the probability of transmission failure w.r.t. the total number of retransmissions attempts.

A paper describing the probabilistic extension of MCL and of the on-the-fly model checker was published in an international journal [13].