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Turing machines are not physical objects, but mathematical ones.

They show if and how any given algorithm can be computed. Turing machines are state machines, where a state represents a position in a graph. State machines use various states, or graph positions, to determine the outcome of the algorithm. To accomplish this, a theoretical one-dimensional tape is said to be divided into an infinite number of cells.

Each cell contains a binary digit, 1 or 0. As the read/write head of the machine scans in the subsequent value in the cell, it uses this value to determine what state to transition to next.

To accomplish this, the machine follows an input of rules, usually in the form of tables, that contain logic similar to: if the machine is in state A and a 0 is read in, the machine is going to go to the next state, say, state B.

The rules that the machines must follow are considered the program. These Turing machines helped define the logic behind modern computer science. Memory in modern computers is represented by the infinite tape, and the bus of the machine is represented by the read/write head.

Turing focused heavily on designing a machine that could determine what can be computed. Turing concluded that as long as a Turing machine exists that could compute a precise approximation of the number, that value was computable.

This does include constants such as pi. Furthermore, functions can be computable when determining TRUE or FALSE for any given parameters.

One example of this would be a function “IsEven”. If this function were passed a number, the computation would produce TRUE if the number were even and FALSE if the number were odd.

Using these specifications, Turing machines can determine if a function is computable and terminate if said function is computable. Furthermore, Turing machines can interpret logic operators, such as “AND, OR, XOR, NOT, and IF-THEN-ELSE”[17] to determine if a function is computable.
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