LSV Seminar

The LSV seminar takes place on Tuesday at 11:00 AM. The usual location is the conference room at Pavillon des Jardins (venue). If you wish to be informed by e-mail about upcoming seminars, please contact Stéphane Le Roux and Matthias Fuegger.

The seminar is open to public and does not require any form of registration.

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A tetrachotomy for positive equality-free logic

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 Barnaby Martin
Monday, March 12 2012 at 02:00PM
Salle de Conférence (Pavillon des Jardins)
Barnaby Martin (Durham University, UK)

We consider the problem of evaluating positive equality-free sentences of FO on a fixed, finite relational structure B. This may be seen as a generalisation of the Quantified Constraint Satisfaction Problem (QCSP), itself a generalisation of the Constraint Satisfaction Problem (CSP). We argue that our generalisation is not totally arbitrary, and that ours is the only problem in a large class - other than the CSP and QCSP - whose complexity taxonomy was unsolved.

We introduce surjective hyper-endomorphisms in order to give a Galois connection that characterises definability in positive equality-free FO. Through the algebraic method we are able to characterise the complexity of our problem for all finite structures B. Specifically, the problem is either in Logspace, NP-complete, co-NP-complete or Pspace-complete.

The problem appears obtuse, but possesses a surprising elegance. There may yet be lessons to be learnt in the methodology of the solution of this case, for the continuing program for CSP.

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