L (complexity) said to be the same as SL
Complete problems and logical characterization
Every non-trivial problem in L is complete under log-space reductions, so weaker reductions are required to identify meaningful notions of L-completeness, the most common being first-order reductions.
A 2004 result by Omer Reingold shows that USTCON, the problem of whether there exists a path between two vertices in a given undirected graph, is in L, showing that L = SL, since USTCON is SL-complete.One consequence of this is a simple logical characterization of L: it contains precisely those languages expressible in first-order logic with an added commutative transitive closure operator (in graph theoretical terms, this turns every connected component into a clique). This result has application to database query languages: data complexity of a query is defined as the complexity of answering a fixed query considering the data size as the variable input. For this measure, queries against relational databases with complete information (having no notion of nulls) as expressed for instance in relational algebra are in L.