### **Internship Opportunities**

Silent Self-Stabilizing Algorithms: Certification Using Coq

### *Scientific Context*

Modern distributed systems can be *large-scale*, *dynamic*,
and / or *resource constrained*. These characteristics make them
more vulnerable to faults. Now, the scale of these systems as well as
the adversarial environment where they may be deployed limit the
possibility of human intervention to repair them. In this context,
fault-tolerance, *i.e.*, the ability of a distributed algorithm to
withstand faults, is mandatory.

Self-stabilization is a versatile lightweight technique to withstand transient faults in a distributed system: a self-stabilizing algorithm recovers correct behavior within finite time after transient faults. Self-stabilization makes no hypotheses on the nature or extent of transient faults that could hit the system, and recovers from the effects of those faults in a unified manner. Therefore the property of self-stabilization is very attractive for a distributed algorithm.

The correctness of self-stabilizing algorithms is often tricky to
establish. It is even more complex and subtle as today’s research on
self-stabilizing focuses on more adversarial environments.
Now, the proof that a distributed algorithm actually achieves a
self-stabilizing property is usually performed by hand, using informal
reasoning. Such methods are clearly pushed to their limits. This
justifies the use of a *proof assistant*, a program which allows
to mechanically verify proofs.
Proof assistants are environments where a user can express
programs, state theorems, and develop proofs interactively, those ones
being mechanically checked (that is, machine-checked). In this project, we use
the Coq proof assistant.

### *Project Summary*

**PADEC** aims at supporting an emerging collaboration between three
researchers. The long-term goal of the collaboration is to propose a
*framework, based on Coq, to (semi-) automatically construct
certified proofs of self-stabilizing properties*.
Such a framework will have to be applicable to a large set of existing
algorithms implementing self-stabilizing properties. Of course, this
framework should propose techniques to address correctness (including
termination) of algorithms, but also quantitative properties, such as
bounds on the stabilization time and optimality of the computed
solutions.
The aforementioned techniques should be applicable to specific
algorithms as well as large classes of algorithms, *e.g.*,
expressed as parametric algorithms or composite algorithms.
We also want to consider more theoretical results such as lower
complexity bounds, impossibility results, and necessary conditions for
different classes of self-stabilizing algorithms.

**Keywords:** Distributed Algorithms, Self-Stabilization, Certified Proofs, Coq.

### *Members*

**Faculties**

- Karine Altisen, Grenoble INP—Verimag
- Pierre Corbineau, UJF—Verimag
- Stéphane Devismes, UJF—Verimag

**Interns**

- X. Montillet - Proving Self-Stabilization in Coq: A Case Study - 2014 (L3)
- A. Chenon - Composition of Self-Stabilizing Algorithms in Coq - 2015 (M1)