There are many different, but equivalent, computational models. I assume that their equivalence is shown by encoding the input of one model with the input of the other model and by arguing why the same algorithm should be available that would solve the problem in this model (eg emulation). ,

I was wondering if there is a computational model that is Turing equivalent, but coding the standard input into its input would be an unpredictable problem. Basically, it is a computational model that is cut off from conventional models by the fact that its encoding is unpredictable. That would be the first part of my question. I

For the second part, if such a model exists, we call it $ S $, you can find other calculation models $ S_0, S_1, dots $so that the conversion between $ S $ and $ S_i $ would be calculable by both $ S $ and $ S_i $? If $ T, T_0, T_1, dots $ Would models of Turing machines and other conventional computing models, would $ mathcal {T} = {T, T_0, T_1, dots } $ and $ mathcal {S} = {S, S_0, S_1, dots } $ be two separate "islands" of the calculation? Both are synonymous, but no member of one of the families would be able to encode his input to the other family. Or maybe only $ mathcal {S} $ would be able to make such a subset of such families of computational models, such as: $ mathcal {T} < mathcal {S} $?

Note: I am not sure if it is formal to talk about a mathematical model as a mathematical model. I've mostly meant most of the last paragraph informally, but perhaps it would be enough just to take a set of all instances of such a computational model. To like $ T = { text {all Turing machines} } $. $ T_0 = { text {all lambda expressions} } $ and such.