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ACTIVITÉS DE RECHERCHE / RESEARCH ACTIVITIES :
Complex Systems and Discrete Dynamical Systems
The definitions of Complex Systems often involve a multitude of simple agents interacting
locally; a complex global behavior emerges from these local interactions. These few ingredients (simple
agents, local interactions, complex global behavior) are typical characteristics of a well-known framework
for discrete dynamical systems, namely cellular automata (CA).
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Bio-inspired Complex Systems
Bio-inspired complex systems fall within the field of complex systems and stochastic
combinatorial optimization by metaheuristics. Our goal is to address such problems and the associated
solving methods, such as evolutionary algorithms, simulated annealing, tabu search, etc., from the
perspective of complex systems.
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Automata, languages, combinatorics, and logic
This research deals with formal languages and automata theory. We consider rational
languages of infinite words which are recognized by Büchi and Muller automata. An ω-language can
be obtained from a classical formal language by the application to its words of the operation of infinite
concatenation denoted .ω.
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3D biological modeling and cellular automata
All biological network models are based on a notion of state that is entirely defined by the
concentration level of each considered biomolecule in the cell. Consequently the spatial arrangement of these molecules and the internal compartments delimited by membranes are ignored in these models.
The best we can do is to introduce two different symbols for the same molecule, depending on the
compartment where it resides, but the evolution rules become often ad hoc.
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Constraint based program verification
Verification is one of the most critical issues in the software engineering process. Numerous
techniques ranging from formal proofs to testing methods have been used during the last years
to verify the conformity of a program with its specification. Recently, constraint programming techniques
have been used to generate test data. In this context, we investigated constraint-based bounded model
checking and forward computations in Hoare Logic.
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Constraints Techniques and Applications
Interval methods have shown their ability to locate and prove the existence of global
optima in a safe and rigorous way. Unfortunately, these methods are rather slow. To boost interval
methods, we developed new filtering techniques. We also investigated the capabilities of constraint
programming over continous domains in rigorous global optimization, as well as in different applications.
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Formal methods applied to the dynamics of genetic networks
Interactions between genes govern deeply the behaviour of a cell but it is a fact that it
would not be sufficient to study independently each interaction in order to “predict” the behaviour of a
cell. Predictive models must address each biological function as the dynamics of a network of genes
as a whole. The first rigorous models
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