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Description
How much memory does a quantum device need to tell two multi-time processes apart? We study process discrimination in a realistic regime where the probing device is reusable, time-homogeneous, and limited to finite coherent memory. While the strategy norm captures the ultimate power of arbitrary adaptive testers, it generally presumes step-dependent control and unbounded quantum memory. We introduce \emph{machines for autonomous distinction} (MADs), a class of fixed devices that probe a process step after step using the same quantum instrument, a coherent memory of dimension $d_a$, and a complete classical record for the final optimal decision. This defines a hierarchy of operational distinguishability measures. We prove that, for any finite horizon $N$, every admissible $N$-step tester can be compiled into a single MAD with an internal clock and sufficiently large memory, implying that the hierarchy increases with $d_a$ and reaches the strategy norm at fixed $N$. For stationary repeated-interaction processes, we further derive a one-step transfer-map description that generates co-emission probabilities for two simultaneous processes and bounds the optimal discrimination success probability. Simulations for a qubit model show explicitly how added coherent memory and internal time-keeping close the gap to fully general adaptive discrimination.