The boolean hierarchy of NP-partitions

Authors:
Sven Kosub;Klaus W. Wagner
Affiliations:
Fakultät für Informatik, Technische Universität München, Boltzmannstraße 3, D-85748 Garching b. München, Germany;Theoretische Informatik, Julius-Maximilians-Universität Würzburg, Am Hubland, D-97074 Würzburg, Germany
Venue:
Information and Computation
Year:
2008

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Abstract

We introduce the boolean hierarchy of k-partitions over NP for k=3 as a generalization of the boolean hierarchy of sets (i.e., 2-partitions) over NP. Whereas the structure of the latter hierarchy is rather simple the structure of the boolean hierarchy of k-partitions over NP for k=3 turns out to be much more complicated. We formulate the Embedding Conjecture which enables us to get a complete idea of this structure. This conjecture is supported by several partial results.