Definition:Balanced String/Definition 2

Definition
Let $S$ be a string in an alphabet containing brackets.

$S$ is said to be balanced it satisfies the following:
 * $(1): \quad$ The null string $\epsilon$ is a balanced string.
 * $(2): \quad$ If $x$ is a symbol that is specifically not a bracket, then the string consisting just of $x$ is a balanced string.
 * $(3): \quad$ If $S$ is a balanced string, then $\paren S$ is a balanced string.
 * $(4): \quad$ If $S$ and $T$ are balanced strings, then $S T$ is a balanced string.
 * $(5): \quad$ Nothing is a balanced string unless it has been created by one of the rules $(1)$ to $(4)$.

Also see

 * Equivalence of Definitions of Balanced String