Logic (also called “synchronizing logic”) in a co-processor (that provides an interface to memory) receives a signal (called a “declaration”) from each of a number of tasks, based on an initial determination of one or more paths (also called “code paths”) in an instruction stream (e.g. originating from a high-level software program or from low-level microcode) that a task is likely to follow. Once a task (also called “disabled” task) declares its lack of a future need to access a shared data, the synchronizing logic allows that shared data to be accessed by other tasks (also called “needy” tasks) that have indicated their need to access the same. Moreover, the synchronizing logic also allows the shared data to be accessed by the other needy tasks on completion of access of the shared data by a current task (assuming the current task was also a needy task).