Encyclopedia of Database Systems

2018 Edition
| Editors: Ling Liu, M. Tamer Özsu

Ehrenfeucht-Fraïssé Games

  • Nicole SchweikardtEmail author
Reference work entry
DOI: https://doi.org/10.1007/978-1-4614-8265-9_1271


EF-games; Ehrenfeucht games


The Ehrenfeucht-Fraïssé game (EF-game, for short) is played by two players, usually called the spoiler and the duplicator (in the literature, the two players are sometimes also called Samson and Delilah or, simply, player I and player II). The board of the game consists of two structures 𝒜 and ℬ of the same vocabulary. The spoiler’s intention is to show a difference between the two structures, while the duplicator tries to make them look alike.

The rules of the classical EF-game are as follows: The players play a certain number r of rounds. Each round i consists of two steps. First, the spoiler chooses either an element ai in the universe of 𝒜 or an element bi in the universe of ℬ. Afterwards, the duplicator chooses an element in the other structure, i.e., she chooses an element bi in the universe of ℬ if the spoiler’s move was in 𝒜, respectively, an element ai in the universe of 𝒜 if the spoiler’s move was in ℬ.

After rrounds, the...

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Recommended Reading

  1. 1.
    Ehrenfeucht A. An application of games to the completeness problem for formalized theories. Fundam Math. 1961;49(2):129–41.MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Fagin R. Easier ways to win logical games. In: Immerman N, Kolaitis PG, editors. Descriptive complexity and finite models, DIMACS Series in Discrete Mathematics and Theoretical Computer Science 31. Providence: American Mathematical Society; 1997. p. 1–32.Google Scholar
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    Fraïssé R. Sur quelques classifications des systèmes de relations. Université d’Alger, Publications Scientifiques; 1954, SérieA(1):35–182.Google Scholar
  4. 4.
    Libkin L. Elements of finite model theory. Berlin: Springer; 2004.zbMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Johann Wolfgang Goethe-University, Frankfurt am MainFrankfurtGermany

Section editors and affiliations

  • Leonid Libkin
    • 1
  1. 1.School of InformaticsUniversity of EdinburghEdinburghUK