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Majority constraints have bounded pathwidth duality.

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We study certain constraint satisfaction problems which are the problems of deciding whether there exists a homomorphism from a given relational structure to a fixed structure with a majority polymorphism. We show that such a problem is equivalent to deciding whether the given structure admits a homomorphism from an obstruction belonging to a certain class of structures of bounded pathwidth. This implies that the constraint satisfaction problem for any fixed structure with a majority polymorphism is in NL.

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