NL-complete

In computational complexity theory, NL-Complete is a complexity class which is complete for NL. It contains the most "difficult" or "expressive" problems in NL. If a method exists for solving any one of the NL-complete problems in logarithmic memory space, then NL=L.

One important NL-complete problem is ST-connectivity (or "Reachability") (Papadimitriou 1994 Thrm. 16.2), the problem of determining whether, given a directed graph G and two nodes s and t on that graph, there is a path from s to t. ST-connectivity can be seen to be in NL, because we start at the node s and nondeterministically walk to every other reachable node. ST-connectivity can be seen to be NL-hard by considering the computation state graph of any other NL algorithm, and considering that the other algorithm will accept if and only if there is a (nondetermistic) path from the starting state to an accepting state.

Another important NL-complete problem is 2-satisfiability (Papadimitriou 1994 Thrm. 16.3), the problem of determining whether a boolean formula in conjunctive normal form with two variables per clause is satisfiable.

References

Papadimitriou, Christos H. (1994). Computational Complexity, Reading, Massachusetts: Addison-Wesley. ISBN 0-201-53082-1.