Question

When does a string belong to the set of bit strings defined recursively by

$\lambda \in \mathbf{A}$

$\mathbf{0}\mathbf{x}\mathbf{1}\mathbf{\in }\mathbf{A}\mathbf{}\mathbf{if}\mathbf{}\mathbf{x}\mathbf{\in }\mathbf{A}$ , where$\mathbf{\lambda }$ is the empty string?

Short answer

The recursive definition of strings is derived.

Step-by-step solution

Define recursive and reversal of the string

The recursive function is one that have its values at some specific points obtained by some previous points. Consider the example for the recursive function f(k) = f (k - 2) + f (k - 3) is define over the non-negative integer.

The string is the set of numbers for exampleabcd is the string where all four variables can take up any values.

Consider the reversal $w^R$of the string is the string written in reverse order.

Find when the string belong the set recursively

Consider the string consists of n number of 0’s followed by number of 1’s for some non-negative integer n, then a string belong to the set of bit string defined recursively by

$x\in A$

$0\mathrm{x}1\in \mathrm{A}\mathrm{if}\mathrm{x}\in \mathrm{A}$

Here, $\lambda$is the empty string.

Hence, the recursive definition of strings is derived.