A decision problem is NL-complete when it belongs to NL and every problem in NL reduces to it by a deterministic logarithmic-space many-one reduction.
The directed graph reachability problem asks whether a directed graph contains a directed path from a specified vertex to a specified vertex . It is NL-complete.
The configuration graph of a machine on a fixed input has one vertex for each machine configuration and a directed edge for each valid computation step.
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