We develop new methods to statically bound the resources needed for the execution of systems of concurrent, interactive threads. Our study is concerned with a \emph{synchronous} model of interaction based on cooperative threads whose execution proceeds in synchronous rounds called instants. Our contribution is a system of compositional static analyses to guarantee that each instant terminates and to bound the size of the values computed by the system as a function of the size of its parameters at the beginning of the instant.
Our method generalises an approach designed for first-order functional languages that relies on a combination of standard termination techniques for term rewriting systems and an analysis of the size of the computed values based on the notion of quasi-interpretation.
We show that these two methods can be combined to obtain an explicit polynomial bound on the space needed for the execution of the system during an instant. We also provide evidence for the expressivity of our synchronous programming model and describe a bytecode for a related virtual machine.