  Type systems as a way to control or analyze programs have been largely
studied in the context of functional programming languages. Some of those work
allow to extract from a typing derivation for a program a complexity bound on
this program. We present how to adapt this result for parallel complexity in
the pi-calculus, as a model of concurrency and parallel communication. We study
two notions of time complexity: the total computation time without parallelism
(the work) and the computation time under maximal parallelism (the span). We
define reduction relations in the pi-calculus to capture those two notions, and
we present two type systems from which one can extract a complexity bound on a
process. The type systems are inspired by input/output types and size types,
with temporal information about communications.
