Constraint Satisfaction with Countable Homogeneous Templates

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Constraint Satisfaction with Countable Homogeneous Templates (2003)

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by Manuel Bodirsky , Jaroslav Nesetril

Venue:	IN PROCEEDINGS OF CSL’03
Citations:	42 - 19 self

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@INPROCEEDINGS{Bodirsky03constraintsatisfaction,
    author = {Manuel Bodirsky and Jaroslav Nesetril},
    title = {Constraint Satisfaction with Countable Homogeneous Templates},
    booktitle = {IN PROCEEDINGS OF CSL’03},
    year = {2003},
    pages = {44--57},
    publisher = {Springer}
}

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Abstract

For a fixed countable homogeneous structure we study the computational problem whether a given finite structure of the same relational signature homomorphically maps to . This problem is known as the constraint satisfaction problem CSP( ) for and was intensively studied for finite . We show that - as in the case of finite - the computational complexity of CSP( ) for countable homogeneous is determinded by the clone of polymorphisms of . To this end we prove the following theorem which is of independent interest: The primitive positive definable relations over an !-categorical structure are precisely the relations that are invariant under the polymorphisms of .

Keyphrases

countable homogeneous template constraint satisfaction relational signature computational problem independent interest constraint satisfaction problem csp finite structure primitive positive definable relation computational complexity fixed countable homogeneous structure following theorem categorical structure

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