# Recursive definition of a set of strings.

2,045

You can describe $E_a$ using the regular expression $(aa+ba)^*(a+b+\lambda)$, which translates into a recursive definition with

• Base case: $\lambda, a, b\in E_a$
• Recursive case: if $w\in E_a$, then $aaw, baw\in E_a$.
Share:
2,045

Author by

### user1732558

Updated on August 01, 2022

Need assistant with this problem, Assume that $\Sigma=\{a,b\}$. Give a recursive definition of the set $E_a$ of all the strings $x\in\Sigma^*$ such that all the symbols occurring at the even positions in $x$ are equal to $a$. I know that Base case $\lambda$ $\epsilon$ $\Sigma^*$ but where should I go from there.
Would I not be able to get $ba\lambda \in E_a$, which has a $b$ as the second (i.e. an even position) letter?
But $ba$ ($\lambda$ being the empty string) has an a as its second letter...