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.