Here you find some words on the subjects I am actually interested in:

Concurrent programs have in the general case a complex control structure although many formalisms
impose an acyclic control graph. We are interested in two related albeit distinct questions about
such computation DAGs: the number of its computation paths and the uniform random generation of such paths.
xThese questions are very difficult for general DAGs, and we thus study interesting subclasses.

Write a random boolean expression on given sets of boolean variables and of connectors:
we obtain a boolean function. How random is this boolean function?
E.g., what is the probability that we obtain a tautology? A literal? Any specified function?
Is the probability of obtaining a given function related to the complexity of the function?
Does the Shannon effect, i.e. the fact that ``almost all'' functions have maximal complexity,
still hold for this probability distribution?

We are interested in two distinct types of structures: tree structures and their associated DAGs
induced by sharing all the identical subtrees. Two classical questions arise in this context.
Sample uniformly a large tree and compact it into a DAG: what is the typical size of the DAGs?
This question is our main interest in the context of binary tries.
Another approach deals directly with a class of compacted objects. Among all DAGs of the same size,
what are the typical measures (e.g. the in or outdegree distribution, the profile...).
What about the enumeration if we restrict to important subclasses of DAGs,
like binary decision diagrams (an efficient way of representing boolean functions in practice) ?

