# What is a universal Turing machine

##

Universal Turing machines

**Next:**Algorithmic Information Theory - Kolmogoroff Complexity

**Up:**Effective predictability and the

**Previous:**Algorithms are general procedures

As explained in the first section, each algorithm can be described by a suitable Turing machine table. The operation table itself can be interpreted mechanically. So the idea is obvious, a Turing machine

*U*to develop which is the operation table of any Turing machine

*T*can interpret and with it

*T*simulated. Such a Turing machine

*U*is also called the universal Turing machine. A universal Turing machine corresponds in its functionality to today's universal computers, which can be reprogrammed as required and then execute their new program. In the following, general considerations will be made about the possibilities of algorithms. In return, the universal Turing machine offers the particular advantage that one can rely on

__a__specific operation table and only has to start from the various possible entries. Thus, all other Turing machines are also taken into account through the possibility of corresponding inputs for the universal Turing machine.

A variant of the so-called *Universal Turing Machine Theorems*^{4.14} is the following:

**theorem** There is a universal Turing machine *U*that computes the following two-digit function: where applies: Let *T*(*A.*) a suitable and calculable coding of the Turing machine table of the algorithm *A.* and *e* any natural number. Then applies *U*(*T*(*A.*),*e*)=*A.*(*e*). *U* thus calculates exactly the value that the algorithm has for its two arguments (an algorithm and an input) as the output value *A.* for input *e* would calculate.

Should a certain algorithm *A.* on a given input string *e*- for example a set of axioms - are applied, this can be done by means of a universal Turing machine *U* So do it as follows: You write both the operation table *T*(*A.*) the Turing machine realization of *A.* and input *e* For *A.* as input to the working tape of *U*. See figure 3.3.

The result of applying the algorithm

*A.*on the input

*e*becomes a possibly infinite string

*r*=

*A.*(

*e*) be that

*U*writes in a specified area of their work tape. So you can establish a relationship between the input of

*U*, namely

*T*(

*A.*) linked to

*e*and the output

*r*of

*U*produce. Furthermore, the relationship of the number of input characters for

*U*and the length and structure of

*r*produce. This relationship is examined in algorithmic information theory.

**Next:**Algorithmic Information Theory - Kolmogoroff Complexity

**Up:**Effective predictability and the

**Previous:**Algorithms are general procedures

*Achim Hoffmann*

*2002-07-12*

- Do German Shepherds prefer German food
- Why do we have incest
- What are property investments
- What kind of bird can bark
- How can I have a body shape
- How to call France from USA
- Is it subjective to perceive someone as intelligent?
- Where can I download the factfulness PDF format
- How does our little brain manage everything
- Can you take SAT exams online
- Who has the oldest Bhagavad Gita
- What makes a composer professional
- How are you baptized?
- How do greenhouses stay warm?
- Deadpool dies in the comics
- Which elective is better
- How is AAFT Noida
- When can we think that we have been reached
- Do Americans have Christmas parties at work
- What is a Yulee Broker
- How is matcha green tea powder made
- Why is matplotlib used
- What are IIT JEE physics best mnemonics
- What is roof repair