Comment by vidarh

If your argument is that a system incorporating a model is not an LLM if there is a loop around it, then reasoning models are not LLMs.

They can do lookup in a table with 100% reliability, yes, because you can make then 100% deterministic if you wish by using numerically stable inferencing code and setting temperature to 0.

Finite context is irrelevant, because the context can be used as an IO channel.

A Turing machine does not have infinite state within the mechanism itself - it requires access to a potentially infinite tape. A Turing machine can be constructed with down to 1 bit of state (a (2,3) or (3,2) Turing machine are the smalles possible, where one number represents the number of states, and the other represents number of discrete symbols it can handle).

An IO channel is computationally equivalent to an infite tape, and unlike an infinite tape, an IO channel is physically possible.