Question

Give a recursive definition of ${\mathbf{w}}^{\mathbf{i}}$, where w is a string and is a nonnegative integer. (Here represents the concatenation of copies of the string .)

Short answer

Recursive definition$w^i$ of is $W^R=W\left(W^{n-1}\right)$.

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) + (k-3) is define over the non-negative integer.

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

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

Find a recursive definition of  wi

Objective of the question is write a recursive definition of $w^i$where is a string and is a nonnegative integer.

Definition of recursive as follow;

Basic step is as follow: $w^0=\lambda$

Recursive step is as follows $w^n=w\left(w^{n-1}\right)$

Hence,recursive definition of $w^i$is $W^R=W\left(W^{n-1}\right)$.