Embodiments of the invention improve the efficiency of communication processing between a host and a storage device. In one embodiment, a data processing system includes a storage device and a host. The host gives the storage device an instruction to perform specified processing, and an instruction as to whether or not a completion notification of the instructed processing is to be transmitted to the host. If the host instructs the storage device to transmit a processing completion notification, the storage device transmits the completion notification to the host. On the other hand, if the host instructs the storage device not to transmit a processing completion notification, the storage device does not transmit the completion notification to the host.