Introduction to Turing Machines in English | Turing Machine Definition | Automata Theory | TOC

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Turing machine is a theoretical model of a computer proposed by mathematician Alan Turing in 1936. It is a simple but powerful machine that consists of an infinite tape divided into cells, a read/write head that can move along the tape, and a control unit that reads and interprets instructions.

The tape of a Turing machine is initially blank, and the control unit reads instructions from a table of rules to determine its actions. These rules specify how the control unit should move the read/write head along the tape and what symbols to write or read at each cell. The control unit can also change its internal state based on the instructions it reads.

A Turing machine can simulate any algorithmic process, making it a fundamental tool in theoretical computer science. It is often used to prove theorems about computability, complexity, and decidability. The Church-Turing thesis, which states that any algorithmic process can be computed by a Turing machine, is a cornerstone of computer science theory.

A TM can be formally defined as a 7-tuple (Q, Σ, Γ, δ, q0, B, F), where:

Q is a finite set of states.
Σ is a finite set of input symbols, also known as the alphabet.
Γ is a finite set of tape symbols.
δ is a transition function that maps Q x Σ: Q x Γ x (L/R)
q0 is the initial state.
B is Blank.
F is the set of final (or accepting) states.

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