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CSL

2003

Springer

2003

Springer

For a ﬁxed countable homogeneous relational structure Γ we study the computational problem whether a given ﬁnite structure of the same signature homomorphically maps to Γ. This problem is known as the constraint satisfaction problem CSP(Γ) for the template Γ and has been intensively studied for ﬁnite Γ. We show that — as in the case of ﬁnite Γ — the computational complexity of CSP(Γ) for countable homogeneous Γ is determined by the clone of polymorphisms of Γ. To this end we prove the following theorem, which is of independent interest: the primitive positive deﬁnable relations over an ω-categorical structure Γ are precisely the relations that are preserved by the polymorphisms of Γ. If the age of Γ is given by a ﬁnite number of ﬁnite forbidden induced substructures, then CSP(Γ) is in NP. We use a classiﬁcation result by Cherlin and prove that in this case every constraint satisfaction problem for a countable homogeneous digraph is either tractable or...

Added |
06 Jul 2010 |

Updated |
06 Jul 2010 |

Type |
Conference |

Year |
2003 |

Where |
CSL |

Authors |
Manuel Bodirsky, Jaroslav Nesetril |

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