Two-way infinite tape turing machine and its power

Definition of two-way infinite tape turing machine
A two-way infinite tape Turing machine is a type of Turing machine that has an infinite tape that extends infinitely in both directions. This means that the tape has no endpoints, and it can be moved in both directions, left and right.

Comparison with basic model of turing machine
In terms of power, the two-way infinite tape Turing machine is not superior to the basic model of the Turing machine. Both machines are equivalent in terms of their computational power. This means that any problem that can be solved by a two-way infinite tape Turing machine can also be solved by a basic model Turing machine, and vice versa.

Explanation
The basic model of the Turing machine has a one-way infinite tape, which can only be moved in one direction, usually to the right. The two-way infinite tape Turing machine, on the other hand, can move the tape in both directions. This may seem like an advantage, but it does not give the machine any extra power.

The reason for this is that any input string can always be written on the tape such that the head of the machine is at the leftmost position. This means that the machine can always move the tape to the right to read the input, and then move back to the left to perform its computations. In other words, the machine can simulate a two-way infinite tape using a one-way infinite tape.

Conclusion
In conclusion, the two-way infinite tape Turing machine is not superior to the basic model of the Turing machine in terms of power. Both machines are equivalent in terms of their computational power, and any problem that can be solved by one machine can also be solved by the other.