# Is a String with no parantheses considered having balanced parantheses?

Say I have a language over the alphabet {x,y,(,)} . The language's rules are: any string over that alphabet with balanced parentheses.

Clearly x(), (xy) , ()()xxx, ((xx)) are accepted. BUT

My question is, is a string with no parentheses considered as having balanced parentheses? For example are: y, xxyy, xyxyxxx accepted?

And then also what about an empty String?

\begin{align*} &S \to \epsilon \\ &S \to xS \\ &S \to yS \\ &S \to (S)S \end{align*}