Universal turing machine U should determine if M(x) stops

Question

so we have a universal turing machine U, that should determine if a turing machine M with input x will stop. The solution should be presented in pseudo code.

can someone help me a bit out, who should i solve it ?

Answer 1

This sounds like the halting problem:

The halting problem can be stated as follows: "Given a description of an arbitrary computer program, decide whether the program finishes running or continues to run forever". This is equivalent to the problem of deciding, given a program and an input, whether the program will eventually halt when run with that input, or will run forever.

Alan Turing proved in 1936 that a general algorithm to solve the halting problem for all possible program-input pairs cannot exist. A key part of the proof was a mathematical definition of a computer and program, what became known as a Turing machine; the halting problem is undecidable over Turing machines.

So no, it's not possible.

If you want, you can probably run M on x for a while. If it stops, we know it stops. If it doesn't stop, we don't really know whether or not it stops.