In computational complexity theory, LOGCFL is the complexity class that contains all decision problems that can be reduced in logarithmic space to a context-free language. This class is closed under complementation. It is situated between NL and AC<sup>1</sup>, in the sense that it contains the former and is contained in the latter. Problems that are complete for LOGCFL include many problems that can be characterized by acyclic hypergraphs:
LOGCFL is the set of decision problems solvable by nondeterministic auxiliary pushdown automata in log space and polynomial time.