An extended OpenMP programming model for cyber-physical systems that includes features for replication and predictable execution based on a new execution concept named Taskgraph. This concept exploits the Task Dependency Graph (TDG) representation of an OpenMP task-based code to replace the user code by an execution completely driven by the OpenMP runtime which (1) alleviates overheads and contention, (2) enables timing analysis of programs under schedulers based on Direct Acyclic Graphs (DAGs) of tasks, and facilitates correctness analysis checking of the parallel representation to avoid inconsistencies and data race conditions. The Taskgraph framework includes features at the syntax and implementation levels, the latter including compiler and runtime support, as presented in the TPDS journal.