  In this paper we characterize two-dimensional semi-log canonical
hypersurfaces in arbitrary characteristic from the viewpoint of the initial
term of the defining equation. As an application, we prove a conjecture about a
uniform bound of divisors computing minimal log discrepancies for two
dimensional varieties, which is a conjecture by Ishii and also a special case
of the conjecture by Musta\c{t}\v{a}-Nakamura.
