Language, Logic, and Computation by Unknown

Author:Unknown
Language: eng
Format: epub
ISBN: 9783662595657
Publisher: Springer Berlin Heidelberg

The following lemma is an analogue of Lemma 1 for switch models.

Lemma 2

Consider and two grid models and . If and , then .

Proof

We will define a winning strategy for D applicable to both the games and . The trick of the strategy consists in preserving the following invariants throughout the game.

1.The info states in the current position are the same.

2.Identity traces coincide in each coordinate: i.e., given and the sequences in the current position, we have and .

By Proposition 3, preserving the invariants ensures the victory of player D. The winning strategy for D is the following:If S plays a -move and chooses s: D chooses s in the other model. This ensures the invariant is preserved.

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