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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