What are the basic ideas of Turing machines?

The basic idea of ​​a Turing machine is: 1. A read-write head with an infinitely long paper tape. The read-write head can move on the paper tape and read or write symbols; 2. How many Turing machines have there? states, including start state, acceptance state, rejection state, etc.; 3. Turing machine can accept input and perform calculations based on input and state transition rules.

# Operating system for this tutorial: Windows 10 system, Dell G3 computer.

The Turing machine is a theoretical computing model proposed by the British mathematician Alan Turing in 1936. The basic idea of ​​Turing machine is to describe the computing process through an ideal abstract model and to study the computing power and computability.

The basic idea of ​​a Turing machine can be summarized as the following points:

1. A read-write head with an infinitely long paper tape: A Turing machine has a tape with an infinite length The paper tape is divided into grids, and each grid can store a symbol. A read-write head can move across the paper tape and read or write symbols.

2. State and state transition rules: Turing machine has multiple states, including start state, acceptance state, rejection state, etc. The state transition rules define how, in a certain state, the Turing machine switches states, writes symbols, and moves the read-write head based on the symbols read by the read-write head.

3. Input and output: A Turing machine can accept input and perform calculations based on input and state transition rules. The calculation results can be reflected in the position of the read-write head and the changes in the symbols on the paper tape. When the Turing machine reaches the acceptance state, it means that the calculation is successful and the result is output, and when it enters the rejection state, it means that the calculation failed.

Based on this basic idea, a Turing machine can simulate the behavior of any computing device, including modern computers. The proposal of Turing machine had a profound impact on computer science and mathematical logic. It laid the foundation for computability theory, automaton theory and complexity theory in the field of computer science.

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