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We analytically investigate the ultrafast dynamic behavior of the proposed optical XNOR and and logic gate devices, composed of a monolithically integrated highly stacked InAs quantum dot semiconductor optical amplifier (SOA) and fabricated with the strain compensation technique and ring resonators. The calculated results indicate that the integrated device can operate in the logic gate functions at 160-Gb/s return-to-zero signals with large eye opening, the value of which is estimated to be 90.3%. This is superior to a bulk-type SOA. We show the potential of this device for routing signal processing, such as signal-label recognition in ultrafast photonic network systems.