Note that the definition of SC differs from P ∩ PolyL, since for the former, it is required that a single algorithm runs in both polynomial time and polylogarithmic space; while for the latter, two separate algorithms will suffice: one that runs in polynomial time, and another that runs in polylogarithmic space.
DCFL, the strict subset of context-free languages recognized by deterministic pushdown automata, is contained in SC, as shown by Cook in 1979.
[3] It is open if directed st-connectivity is in SC, although it is known to be in P ∩ PolyL (because of a DFS algorithm and Savitch's theorem).
RL and BPL are classes of problems acceptable by probabilistic Turing machines in logarithmic space and polynomial time.
Noam Nisan showed in 1992 the weak derandomization result that both are contained in SC.