A formal semantics is introduced for a Process Network model, which combines streaming and reactive control processing with task parallelism properties suitable to exploit multi-cores. Applications that react to environment stimuli are implemented by communicating sporadic and periodic tasks, programmed independently from an execution platform. Two functionally equivalent semantics are defined, one for sequential execution and one real-time. The former ensures functional determinism by implying precedence constraints between jobs (task executions), hence, the program outputs are independent from the task scheduling. The latter specifies concurrent execution on a real-time platform, guaranteeing all model's constraints; it has been implemented in an executable formal specification language. The model's implementation runs on multi-core embedded systems, and supports integration of runtime managers for shared HW/SW resources (e.g. for controlling QoS, resource interference or power consumption). Finally, a model transformation approach has been developed, which allowed to port and statically schedule a real spacecraft on-board application on an industrial multi-core platform.