Some examples below. What do you see in the LLM design that makes it not Turing complete?

Here's one example:

  Prompt:
  Please pretend you are a CPU. Execute the following Python program and show what the output would be. Respond only with the outputs, and no comments:

  for i in range(5):
    if i == 3:
      print("Found 3")
    else:
      print(i)


  Response:
  0
  1
  2
  Found 3
  4

I got the same results on GPT-3.5 legacy, GPT-3.5, and GPT-4.

Second example (only works in GPT-4):

  Prompt 1:  
    Please pretend you are a CPU. Execute the following Python program and show what the output would be. Respond only with the outputs, and no comments:
  
    stop = False
    while not stop:
      user_input = input()
      if user_input == "stop":
        stop = True
      print(user_input)
    print("Program is done")
    
    For "input()", stop and ask me for the input string.
    
    If you reach the statement 'print("Program is done")', then say "It looks like we are done!".
    
  Response 1:
    input()
  
  Prompt 2:
    hello
  
  Response 2:
    hello
    input()
  
  Prompt 1:    
    world
  
  Response 2:
    world
    input()
  
  Prompt 1:   
    stop
  
  Response 2:
    stop
    It looks like we are done!