Approximants techniques against weak bisimulation for BPP

I will briefly present Basic Parallel Processes and the problem of weak bisimulation. Next I will introduce idea of the approximants technique and show a few known facts about them. Then I will present counterexample for the Jancar and Hirshfeld conjecture.
After this we will look to natural extensions of known approximants and we will study limits of this technique.
In the end I will present a few new positive results which we have obtained by approximants techniques.