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CORR

2010

Springer

2010

Springer

We study the complexity of evaluating positive equality-free sentences of first-order (FO) logic over a fixed, finite structure B. This may be seen as a natural generalisation of the nonuniform quantified constraint satisfaction problem QCSP(B). We introduce surjective hyperendomorphisms and use them in proving a Galois connection that characterises definability in positive equality-free FO. Through an algebraic method, we derive a complete complexity classification for our problems as B ranges over structures of size at most three. Specifically, each problem is either in L, is NP-complete, is co-NP-complete or is Pspace-complete.

Related Content

Added |
09 Dec 2010 |

Updated |
09 Dec 2010 |

Type |
Journal |

Year |
2010 |

Where |
CORR |

Authors |
Florent R. Madelaine, Barnaby Martin |

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