A data processing apparatus 2 includes a programmable general purpose processor 10 coupled to a hardware accelerator 12. A memory system 14, 6, 8 is shared by the processor 10 and the hardware accelerator 12. Memory system monitoring circuitry 16 is responsive to one or more predetermined operations performed by the processor 10 upon the memory system 14, 6, 8 to generate a trigger to the hardware accelerator 12 for it to halt its processing operations and clean any data values held as temporary variables within registers 20 of the hardware accelerator back to the memory system 14, 6, 8.