Complexity Class $\mathsf{D}_2^{\mathsf{P}}$

The decision problems $L = L_1 \cap L_2$ with $L_1 \in \Sigma_2^{\mathsf{P}}$ and $L_2 \in \Pi_2^{\mathsf{P}}$ : the analogue of $\mathsf{DP}$ for $\Sigma_2^{\mathsf{P}}$ and $\Pi_2^{\mathsf{P}}$ , i.e. the second level of the Boolean hierarchy over $\Sigma_2^{\mathsf{P}}$ .

Reference

Chang, R. & Kadin, J. (1996). The Boolean Hierarchy and the Polynomial Hierarchy: A Closer Connection. SIAM Journal on Computing, 25(2), pp. 340–354.

Complexity Class D2P\mathsf{D}_2^{\mathsf{P}}

Reference

Complexity Class $\mathsf{D}_2^{\mathsf{P}}$