- Simulation of Distributed Algorithms
- Local Reasoning about Reconfigurable Component-based Systems
The goal of this internship is the study of logics for the design and verification of complex component-based distributed applications, using the principles of locality (the ability to describe the effect of an update only from the parts involved while gnoring the ones unchanged) and compositionality (the ability to join the results of local analyses into a global condition capturing the correctness requirement for the entire system). During this internship, the candidate will aquire command of advanced theoretical notions of logics and system verification. The internship comprises theoretical as well as implementation work.

- Verifying Concurrent Systems with Automata over Infinite Alphabets
The goal of this internship is to study extensions of finite-state automata over infinite alphabets and apply them to the verification of concurrent and distributed systems with unbounded numbers of threads. The internship comprises theoretical as well as implementation work, and will explore orthogonal domains, such as logic, automata theory and concurrency.

- Decision Procedures for Separation Logic Modulo Theories of Data
The goal of this internship is to study the combination of Separation Logic with data theories supported by SMT solvers. The internship comprises theoretical as well as implementation work.

- PhD position : software vulnerability analysis guided by countermeasures and attacker capabilities
- PhD position : Encoding and Sampling of Constrained Signal Spaces for Validation of CPS
- PhD position : Proving Correctness of Reconfigurable Systems
The goal of this PhD project is the development of a rigourous design framework for distributed systems, that uses verification from the early stages of model building. Formal verification is the process of transforming a query about the correctness of a system (e.g. is every store request to a cloud treated by storing the data in such a way that any future retrieval request will eventually find it ?) into a logical validity query (is a given formula true in general ?) that can be handled by automated reasoning techniques (theorem proving). Hence, we recognise logic, automated reasoning and model checking as being the main ingredients of formal verification, and also central research topics in our project.

The successful candidate is expected to work on logics for high-level reasoning about parameterized architectures of distributed systems. The decision problems of these logics will be studied from a theoretical point of view, such as existence of proof systems and the complexity of related algorithms. The architecture description logics will be used to verify systems by parameterized model checking techniques based on e.g., invariant synthesis and automata learning. We plan on implementing proof-of-concept prototype tools and performing experiments on models of real-life systems (inter-blockchain communication, mobile applications, etc.)

- PhD Position : Decision Procedures for Inductive Separation Logic Modulo Data Theories
The goal of this PhD project is to devise a procedure that is optimal from a theoretical point of view, practically efficient, and able to handle a class of definitions that is as large as possible, combining spatial reasoning (to reason on the shape of the considered data structures) with theory reasoning based on external tools (to take into account the properties of the data stored inside the structure).

- Convex polyhedra in floating point
- Certified compilation for security