Difference between Turing machine and Universal Turing machine
Last Updated :
10 Jan, 2023
Turing Machine was first described by Alan Turing in the year 1936. It was primarily invented to investigate the computability of a given problem. It accepts type-0 grammar which is Recursively Enumerable language. The Turing machine has a tape of infinite length where we can perform read and write operations. The infinite cells of the Turing machine can contain input symbols and blanks. It has a head pointer that can move in any direction, it points to the cell where the input is being read.
Universal Turing Machine simulates a Turing Machine. Universal Turing Machine can be considered as a subset of all the Turing machines, it can match or surpass other Turing machines including itself. Universal Turing Machine is like a single Turing Machine that has a solution to all problems that is computable. It contains a Turing Machine description as input along with an input string, runs the Turing Machine on the input and returns a result.
The difference between Turing Machine and Universal Turing Machine are as follows:
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Turing Machine
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Universal Turing Machine
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1. |
It is a mathematical model of computation it manipulates symbols on the tape according to the rules defined |
Universal Turing Machine is like a single Turing Machine that has a solution to all problem that is computable |
2. |
A program can be compared to a Turing Machine |
Programmable Turing Machine is called Universal Turing Machine |
3. |
Turing machine’s temporary storage is tape. The infinite cells of the Turing machine can contain input symbols and blanks. |
Universal Turing Machine contains Turing Machine description as input along with an input string, runs the Turing Machine on the input and returns the result. |
4. |
Turing machines help us understand the fundamental limitations of mechanical computation power |
Although developed for theoretical reasons, it helped in the development of stored program computers |
5. |
A Turing machine is a formal model of a computer with a fixed program |
Universal Turing Machine provides a solution to problems that are computable |
6. |
It does not minimize the space complexity |
It minimizes space complexity |
7, |
Transition function which Turing Machine performs is defined as: δ X T -> Q X T X {L,R}, where δ is the transition function |
The transition function is Q × T → Q × T × {L, R}, where Q is a finite set of states, T is the tape of the alphabet |
8. |
In the set theory point of view, all Turing machines form a set of the all the device that accepts type 0 grammar |
Universal Turing Machine is a subset of all the Turing Machines |
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