The classes of depthbounded and namebounded processes are fragments of the picalculus for which some of the decision problems that are undecidable for the full calculus become decidable. P is depthbounded at level k if every reduction sequence for P contains successor processes with at most k active nested restrictions. P is namebounded at level k if every reduction sequence for P contains successor processes with at most k active bound names. Membership of these classes of processes is undecidable. In this paper we use binary session types to decise two type systems that give a sound characterization of the properties: If a process is welltyped in our first system, it is depthbounded. If a process is welltyped in our second, more restrictive type system, it will also be namebounded.
