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Difference between Turing machine and Universal Turing machine

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  • Last Updated : 28 Apr, 2022

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 Turning Machine stimulates a Turning 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 Turning Machine description as input along with an input string, runs the Turning Machine on the input and returns a result.

 

The difference between Turing Machine and Universal Turing Machine are as follows: 

 

Turing Machine

Universal Turing Machine

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 Turning Machine description as input along with an input string, runs the Turning 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 Turning Machines
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