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Descriptive Complexity Theory

  • Heinz-Dieter Ebbinghaus
  • Jörg Flum
Part of the Perspectives in Mathematical Logic book series (PML)

Abstract

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
$$ \varphi (x,y): = Exy \vee \exists z(Exz \wedge Ezy) $$
.

Keywords

Turing 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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Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Heinz-Dieter Ebbinghaus
    • 1
  • Jörg Flum
    • 1
  1. 1.Institute of Mathematical LogicUniversity of FreiburgFreiburgGermany

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