Definition:Palindrome/Definition 2

Definition
A palindrome is a string defined as follows:


 * $(1): \quad$ The null string $\epsilon$ is a palindrome.
 * $(2): \quad$ If $a$ is a symbol, then the string $a$ is a palindrome.
 * $(3): \quad$ If $a$ is a symbol and $x$ is a palindrome, then $axa$ is a palindrome.
 * $(4): \quad$ Nothing is a palindrome unless it has been created by one of the rules $(1)$ to $(3)$.

Also see

 * Equivalence of Definitions of Palindrome