The Operational Transformation (OT) approach, used in many collaborative editors, allows a group of users to concurrently update replicas of a shared object and exchange their updates in any order. The basic idea of this approach is to transform any received update operation before its execution on a replica of the object. This transformation aims to ensure the convergence of the different replicas of the object, even if the operations are executed in different orders. However, designing transformation functions for achieving convergence is a critical and challenging issue. Indeed, the transformation functions proposed in the literature are all revealed incorrect. This paper investigates the existence of transformations functions which ensure convergence. From the theoretical point of view, two properties, named TP1 and TP2, are necessary and sufficient to ensure convergence. For the basic signatures of insert and delete operations, we show, using controller synthesis technique, that there are some transformation functions, which satisfy TP1. But, there is no transformation function, which satisfies both TP1 and TP2.