Hardware acceleration of task dependency management in parallel computing, wherein solutions are proposed for hardware-based dependency management to support nested tasks, resolve system deadlocks as a result of memory full conditions in the dedicated hardware memory and synergetic operation of software runtime and hardware acceleration to solve otherwise unsolvable deadlocks when nested tasks are processed. Buffered asynchronous communication of larger data exchange are introduced, requiring less support from multi-core processor elements as opposed to standard access through the multi-core processor elements. A hardware acceleration processor may be implemented in the same silicon die as the multi-core processor for achieving gains in performance, fabrication cost reduction and energy consumption saving during operation.