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Next-generation many-core embedded platforms have the chance of intercepting a converging need for high performance and predictability. Programming methodologies for such platforms will have to promote predictability as a first-class design constraint, along with features for massive parallelism exploitation. OpenMP, increasingly adopted in the embedded systems domain, has recently evolved to deal with the programmability of heterogeneous many-cores, with mature support for fine-grained task parallelism. While tasking is potentially very convenient for coding real-time applications modeled as periodic task graphs, OpenMP adopts an execution model completely agnostic to any timing requirement that the target application may have. In this position paper we reason about the suitability of the current OpenMP v4 specification and execution model to provide timing guarantees in many-cores.