# The Boolean Hierarchy I: Structural Properties

@article{Cai1988TheBH,
title={The Boolean Hierarchy I: Structural Properties},
author={Jin-Yi Cai and Thomas Gundermann and Juris Hartmanis and Lane A. Hemaspaandra and Vivian Sewelson and Klaus W. Wagner and Gerd Wechsung},
journal={SIAM J. Comput.},
year={1988},
volume={17},
pages={1232-1252}
}
In this paper, we study the complexity of sets formed by boolean operations (union, intersection, and complement) on NP sets. These are the sets accepted by trees of hardware with NP predicates as leaves, and together these form the boolean hierarchy.We present many results about the structure of the boolean hierarchy: separation and immunity results, natural complete languages, and structural asymmetries between complementary classes.We show that in some relativized worlds the boolean… Expand
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