Describe an algorithm (not a Turing machine but rather explain in words). We wan

Question

Describe an algorithm (not a Turing machine but rather explain in words). We want to build a description of a Turing machine that accepts {0 2 n | n 0}. For example 0 is in the language for n = 0. also 00 for n = 1. For n = 2 we get that 0000 is in the language. Also 00000000 for n = 3.

Hint: Go over the string and remove every second 0. And then return left. You have to check if the size of the string is not odd.

Let me be clear: You should write an algorithm that says: Go over the list from left to right and remove every second 0, etc. Namely explain in words not build a Turing machine. You should note that if you understand the algorithm, making in a program for a Turing machine is a purely technical matter.

Explanation / Answer

Turning Machine:

A turning machine is a hypothetical machine thought of by the mathemetics Alan.Despite its simplicity,the machine can simulate ANY computeer algorithm,no matter how complicated it is.

It accepts 0^2n|n>=0

for n=0 0^2n|n>=0 => 0

n=0

n=1

n = 2

At any time the machine has a head which is positioned over one of the squares on the tape.with this head the machine can perform three very basic operations:

1.Read the symbol on the square under head

2.Edit symbolby writing a new symbol or erasing it

3.Move the tape left or right by one square so that the machine can read and edit symbol on a neighbour square

n = 3

A trival example let try printing "000"

first write 0 on square under head

Next move tape left by one square

now write 0 on new square under head:

nqw move to left by one square again:

finally write 0 that's it

A simple program

Symbol read Write instruction Move instruction

Blank None None

0 Write 1 move to the right

1 Write 0 move to right

The machine will first read the symbol under head.

The current symbol is 0

Finally a blank symbol is read so the machine does nothing apart from blank symbol continuosly since we have instructed it to repeat the read-write-move sequence withput stopping.

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