Theory Of Computation (2160704)

BE | Semester-7   Winter-2018 | 27/11/2018

Q4) (a)

Write a short note on Universal Turing Machine.

Universal Turning Machine

  • A Universal Turing machine is a Turing machine (Tu) that works as follows:
  • It is assumed to receive an input string of the form e(T)e(z), where T is an arbitrary TM, z is a string over the input alphabet of T , and e is an encoding function whose values are strings in {0,1}*. The computation performed by Tu on this input string satisfies following two properties:
    1. Tu accepts the string e(T)e(z) if and only if T accepts z.
    2. If T accepts z and produces output y, then (Tu) produces output e(y).