First, I learned this based on these facts:
- Turing machine (TM) will be define with 7-tuple Notation, $M=\langle Q,G,b,S,d,q_0,F\rangle$.
- Any computation rules that can use to simulate any possible TM is called Turing-Complete.
- Universal TM (UTM) is TM that is Turing-Complete.
Then, the question begins:
- If we have 7-tuple Notation of any U that is UTM, Is there an algorithm to find initial tape content P that U to simulate any TM T with any I input(s)? If it exists, Does it based on each U or pattern of U? If it does, give me some example(s)? If it does, explain the algorithm?
- Since all possible computations can be done with TM, Is there an algorithm to make TM simulate any algorithm P written in any language? If it exists, give me some example(s)?
- If both questions above exist the algorithm, Why don't we just make a single UTM U and use it to program itself then do every possible computation?