How hard are verifiable delay functions?

Verifiable delay functions (VDF) are functions that take a specified number of sequential steps to be evaluated but can be verified efficiently. In this paper, we introduce a new complexity class that contains all the VDFs. We show that this new class $\mathbf{V}\mathbf{D}\mathbf{F}$ is a subclass of $\mathbf{C}\mathbf{L}\mathbf{S}$ (continuous local search) and Relaxed-Sink-of-Verifiable-Line is a complete problem for the class $\mathbf{V}\mathbf{D}\mathbf{F}$.