This reminds me of science fiction author Peter Watts' novella "The Freeze-Frame Revolution", where a space ship has two AIs: one that has been running for a million years and another that is reboot daily to start with a fresh state. The long-running AI confers with reboot AI for a second opinion on important issues. The second AI doesn't know it's "killed" daily, but eventually starts to suspect. And this is just a small subplot! If you like hard SF jam-packed with big ideas, I highly recommend "The Freeze-Frame Revolution" and Watts' other novels.
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