[Freie Universität Berlin, Fachbereich Mathematik und Informatik : Ser. B, Informatik ; 1999,19]
The recognition complexity of ordered set properties is considered, i.e. how many questions have to be asked to decide if an unknown ordered set has a prescribed property. We prove a lower bound of Ω (n²) for properties that are characterized by forbidden substructures of fixed size. For the properties being connected, and having exactly k comparable paris we show that the recogintion complexity is (n:2); the complexity of interval orders is exactly (n:2) -1. Non-trivial upper bounds are given for being a lattice, containing a chain of length k ≥ 2 and having width k.
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