# A tetrachotomy for positive first-order logic without equality

Madelaine, Florent and Martin, Barnaby
(2011)
*A tetrachotomy for positive first-order logic without equality.*
In:
Logic in Computer Science (LICS), 2011 26th Annual IEEE Symposium on.
IEEE, pp. 311-320.
ISBN 9781457704512.
[Book Section]
(doi:10.1109/LICS.2011.27)

## Abstract

We classify completely the complexity of evaluating positive equality-free sentences of first-order logic over a fixed, finite structure D. This problem may be seen as a natural generalisation of the quantified constraint satisfaction problem QCSP(D). We obtain a tetrachotomy for arbitrary finite structures: each problem is either in L, is NP-complete, is co-NP-complete or is P space-complete. Moreover, its complexity is characterised algebraically in terms of the presence or absence of specific surjective hyper-endomorphisms, and, logically, in terms of relativisation properties with respect to positive equality-free sentences. We prove that the meta-problem, to establish for a specific D into which of the four classes the related problem lies, is NP-hard.

Item Type: | Book Section |
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Additional Information: | Conference details: 26th Annual IEEE Symposium on Logic in Computer Science (LICS 2011), Ontario, Canada, 21-24 June 2011. Proceedings online ISBN: 9780769544120 |

Research Areas: | A. > School of Science and Technology > Computer Science A. > School of Science and Technology > Computer Science > Foundations of Computing group |

Item ID: | 9676 |

Useful Links: | |

Depositing User: | Devika Mohan |

Date Deposited: | 16 Jan 2013 08:49 |

Last Modified: | 24 Apr 2018 14:52 |

URI: | https://eprints.mdx.ac.uk/id/eprint/9676 |

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