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Binary Relations: Finite Characterizations and Computational Complexity

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Abstract

A characterization of a property of binary relations is of finite type if it is stated in terms of ordered T-tuples of alternatives for some positive integer T. The concept was introduced informally by Knoblauch (2005). We give a clear, complete definition below. We prove that a characterization of finite type can be used to determine in polynomial time whether a binary relation over a finite set has the property characterized. We also prove a simple but useful nonexistence theorem and apply it to three examples.

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Authors and Affiliations

  1. Department of Economics, University of Connecticut, Storrs, CT, 06269-1063, USA

    Vicki Knoblauch

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  1. Vicki Knoblauch
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Correspondence to Vicki Knoblauch.

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Knoblauch, V. Binary Relations: Finite Characterizations and Computational Complexity. Theory Decis 65, 27–44 (2008). https://doi.org/10.1007/s11238-007-9079-6

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  • DOI: https://doi.org/10.1007/s11238-007-9079-6

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