A data processing device uses a portion of a random access memory as an input buffer for holding a portion of a stream of data which is being processed by a processing unit within the processing device. Various break-point source tasks 801a-n determine discontinuities in the portion of data stored in the input buffer and a sorted list of the addresses of the discontinuities is maintained in breakpoint queue 800. Since the buffer is managed in a FIFO manner, a single breakpoint register 810 is sufficient to monitor addresses as they are provided by an address register 820 for accessing the random access memory. When a breakpoint is detected, the breakpoint queue and the breakpoint register is updated by an update task 802.