C-hard Decision Problem

Definition

C-hard Decision Problem

A decision problem $\mathcal{P}$ is hard w.r.t. a complexity class $C$ if every decision problem in $C$ can be reduced to $\mathcal{P}$, i.e.,

$$\forall {\mathcal{P}}^{\prime }\in C:P^{\prime }{\le }_m\mathcal{P},$$

where ${\le }_m$ denotes many-one reducibility.