MoL-2017-06: Extensions Of The Garden-hose Model

MoL-2017-06: Koek, Merlijn (2017) Extensions Of The Garden-hose Model. [Report]

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Abstract

This thesis is a study of new models related to the Garden-hose model, in search of new mathematical tools for a better understanding of the Garden-hose complexity. After providing a detailed introduction of the Garden-hose model, we introduce an extension of the model that admits multiple parties. In addition to proving several bounds on the complexity of functions in this new model, we prove the complexity of the 1-bit, k-player equality function. We sketch the applicability of the Multiparty Garden-hose model on a natural multidimensional extension of the position-verification scheme that gave rise to the original Garden-hose model. Furthermore, we introduce the Leaky Garden-hose model, in which Alice and Bob receive more information about the water flow. We prove some results about this model, and define a family of intermediate models where all functions have a complexity between the Garden-hose complexity and the Leaky Garden-hose complexity, thus bridging the gap to the Garden-hose model.

Item Type: Report
Report Nr: MoL-2017-06
Series Name: Master of Logic Thesis (MoL) Series
Year: 2017
Subjects: Computation
Logic
Depositing User: Dr Marco Vervoort
Date Deposited: 06 Jul 2017 15:30
Last Modified: 13 Jul 2017 13:26
URI: https://eprints.illc.uva.nl/id/eprint/1542

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