# Is there a common notation for describing this operation $coNP\; ? \; NP = DP$?

While working with complexity classes, I've come along the definition of $$DP$$ (or $$D^p$$): $$DP = \{L_1 \cap L_2 \mid L_1 \in NP \text{ and } L_2 \in coNP\}$$

I am interested in a different (and much shorter form) of describing this exact operation on class-level, rather than language-level $$coNP\; ? \; NP = DP$$

Since this is different than just cutting both classes, I was wondering what symbol is commonly used for this operation?

In the theory of "abstract families of languages" one uses the notation $$\mathcal K \land \mathcal L$$ to denote the pairwise intersection of languages in $$\mathcal K$$ and $$\mathcal L$$, thus $$\{\;K\cap L\mid K\in\mathcal K \text{ and } L\in\mathcal L\;\}$$.
• Thanks for your Answer! I thought about using $\land$ since it pinpoints to the fact that both languages need to be included in the respective class, but I'm afraid to overload the symbol. Commented Mar 31, 2023 at 16:25