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## Homework Statement

Give a recursive definition for the set

of bit strings [itex]\{ 0^{r} 1^{s} 0^{r} \| r, s \in N \}[/itex]. Note the number of 0’s must be equal, but the

number of 1’s may be different from the number of 0’s.

## Homework Equations

N/A

## The Attempt at a Solution

I believe this is:

Basis: [itex]\lambda \in A[/itex]

Recursive Step: If [itex]\omega \in A[/itex], then [itex]0 \omega 1 \omega 0 \in A[/itex]

I just want to verify if this is correct or not.

Thanks!