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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 \({\cal A}\) and \({\cal B}\) 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 a i in the universe of \({\cal A}\) or an element b i in the universe of \({\cal B}\). Afterwards, the duplicator chooses an element in the other structure, i.e., she chooses an element b i in the universe of \({\cal B}\) if the spoiler’s move was in \({\cal A}\), respectively, an element a...
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Recommended Reading
Ehrenfeucht A. An application of games to the completeness problem for formalized theories. Fundamenta Mathematicae, 49:129–141, 1961.
Fagin R. Easier ways to win logical games. In Descriptive Complexity and Finite Models, N. Immerman, P.G. Kolaitis (eds.). DIMACS Series in Discrete Mathematics and Theoretical Computer Science 31. American Mathematical Society, 1997, pp. 1–32.
Fraïssé R. Sur quelques classifications des systèmes de relations. Université d’Alger, Publications Scientifiques, SérieA(1):35–182, 1954.
Libkin L. Elements of Finite Model Theory. Springer, Berlin, 2004.
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Schweikardt, N. (2009). Ehrenfeucht-Fraïssé Games. In: LIU, L., ÖZSU, M.T. (eds) Encyclopedia of Database Systems. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-39940-9_1271
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DOI: https://doi.org/10.1007/978-0-387-39940-9_1271
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