Section: New Results

Timed, Probabilistic, and Stochastic Extensions

Specifying and verifying quantitative properties of concurrent systems requires expressive and user-friendly property languages combining temporal, data-handling, and quantitative aspects. To this aim, we undertook the quantitative analysis of concurrent systems modeled as PTSs (Probabilistic Transition Systems), whose actions contain channel names, data values, and probabilities. We proposed a new regular probabilistic operator that extends naturally the Until operators of PCTL (Probabilistic Computation Tree Logic)  [41], by specifying the probability measure of a path characterized by a generalized regular formula involving arbitrary computations on data values. We devised an on-the-fly model checking method for this new operator, based on a combined local resolution of linear and Boolean equation systems.

In 2019, we continued this work as follows:

• The MCL v4 language was conservatively extended with the new probabilistic operator, leading to a new version MCL v5.

• A new version 5 of the EVALUATOR model checker that handles the MCL v5 language, was added to CADP. EVALUATOR 5 is backward compatible with EVALUATOR 4, to which it adds a new option “-epsilon ” specifying the precision of floating-point computations. A new version 5 of the MCL_EXPAND tool, the front-end common to the EVALUATOR 3, 4, and 5 model checkers, was added to CADP. This version is upward compatible with the previous one (except for slight changes in some error messages), it corrects a bug and brings some optimizations in the C code generated. Two new manual pages “evaluator5” and  “mcl5” have been added.

• For certain probabilistic formulas (e.g., expressing the step-bounded reachability of events), the on-the-fly model checking procedure can be optimized by taking advantage of the possible query containments, i.e., implications between instances of the formula with different data parameters. We studied query containment in DHMLR (Data-based Hennessy-Milner Logic with Recursion), a parameterized equational formalism used as intermediate language for model checking MCL formulas. Our method consists in detecting, by static analysis, the containment orders present in the DHMLR representation of an MCL formula, and using the information about parameterized Boolean variable implications to improve the convergence of the BES resolution algorithms. We implemented the method in a prototype extension of EVALUATOR 5 and of the CAESAR_SOLVE library for BES resolution, and applied it for verifying probabilistic and also functional properties (e.g., bounded inevitability). The experiments we carried out on self-stabilizing protocols and communication protocols over unreliable channels showed reductions of up to 50% in memory and up to 33% in execution time. This work led to a paper submitted to an international conference.