Descriptive Complexity Theory
Part of the Perspectives in Mathematical Logic book series (PML)
In Chapter 0 we gave the example of a database D that contains the names of the main cities in the world and the pairs (a, b) of cities such that a given airline offers service from a to b without stopover. D may be interpreted as a first-order structure, more precisely, as a digraph G = (G,E G ), where G is the set of cities and E G ab means that there is a flight from a to b without stopover. Now, first-order logic may be viewed as a query language. For example, let
$$ \varphi (x,y): = Exy \vee \exists z(Exz \wedge Ezy) $$
KeywordsTuring Machine Complexity Class Logical Description Transitive Closure Input Tape
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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© Springer-Verlag Berlin Heidelberg 1995