Not exactly about adversarial error correction, but: there is a construction (Çapuni & Gács 2021) of a (class of) universal 1-tape (!!) Turing machine that can perform arbitrarily long computation subject to random noise in the per-step action. Despite the non-adversarial noise model, naive majority error correction (or at least their construction of it) only fixes bounded & local error bursts—meaning it doesn’t work in the general case, because even though majority vote reduces error probability, the effective error rate is still positive, so something almost surely goes wrong (eg error burst of size greater than what majority vote can handle) as T→∞.
Their construction, in fact, looks like a hierarchy of simulated turing machines where the higher-level TM is simulated by a level below it but at a bigger tape scale, such that it can resist larger error bursts—and the overall construction looks like “moving” the “live simulation” of the actual program that we want to execute up the hierarchy over time to coarser and more reliable levels.
Not exactly about adversarial error correction, but: there is a construction (Çapuni & Gács 2021) of a (class of) universal 1-tape (!!) Turing machine that can perform arbitrarily long computation subject to random noise in the per-step action. Despite the non-adversarial noise model, naive majority error correction (or at least their construction of it) only fixes bounded & local error bursts—meaning it doesn’t work in the general case, because even though majority vote reduces error probability, the effective error rate is still positive, so something almost surely goes wrong (eg error burst of size greater than what majority vote can handle) as T→∞.
Their construction, in fact, looks like a hierarchy of simulated turing machines where the higher-level TM is simulated by a level below it but at a bigger tape scale, such that it can resist larger error bursts—and the overall construction looks like “moving” the “live simulation” of the actual program that we want to execute up the hierarchy over time to coarser and more reliable levels.