The context can change each time. To implement a UTM only requires 2 states and 3 symbols or the reverse.
replySo if you use the context not as a tape in itself, but as an io channel to read/write an infinite tape, the context for any given step can remain fixed in size, and so the step itself can be O(1).
Any basic lookup table is turing complete if you bolt an external infinite tape and read/write head onto it. But then that’s moving the goal post since the context wouldn’t be the “limitless tape” and it’s not a transformer “in the normal way” because turing completeness would be coming from external io and not from auto regressive self attention. Different topic.
replyIt's not contradictory at all. The dfa at each step of the turing machine model is also o(1).
replyOf course it is. You’re conflating a turing machine with a transformer. Transformers don’t have a local read/write head. The [self] attention is over the whole context, which makes each step O(N) at best (with caching) and O(N^2) w/o.
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