## Section: New Results

### Making Population Protocols Self-stabilizing

Participants : Joffroy Beauquier, Janna Burman, Shay Kutten, Brigitte Rozoy.

As stated in the previous paragraph, the application domains of the population protocol model are asynchronous large scale networks, in which failures are possible and must be taken into account. This work concerns failures and namely the technique of self-stabilization for tolerating them.

Developing self-stabilizing solutions (and proving them) is considered to be more challenging and complicated than developing classical solutions, where a proper initialization of the variables can be assumed. This remark holds for a large variety of models and hence, to ease the task of the developers, some automatic techniques have been proposed to transform programs into self-stabilizing ones.

We have proposed such a transformer for algorithms in the population protocol model introduced for dealing with resource-limited mobile agents. The model we consider is a variation of the original one in that there is a non mobile agent, the base station, and that the communication characteristics (e.g. moving speed, communication radius) of the agents are considered through the notion of cover time.

The automatic transformer takes as an input an algorithm solving a static problem and outputs a self-stabilizing solution for the same problem. To the best of our knowledge, it is the first time that such a transformer for self-stabilization is presented in the framework of population protocols. We prove that the transformer we propose is correct and we make the complexity analysis of the stabilization time.