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 establish the Embedding Conjecture which enables us to get a complete idea of this structure. This conjecture is supported by several partial results.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
J.-Y. Cai, T. Gundermann, J. Hartmanis, L. A. Hemachandra, V. Sewelson, K. W. Wagner, and G. Wechsung. The boolean hierarchy I: Structural properties. SIAM Journal on Computing, 17(6):1232–1252, 1988.
J.-Y. Cai and L. Hemachandra. The Boolean hierarchy: hardware over NP. In Proceedings 1st Structure in Complexity Theory Conference, volume 223 of Lecture Notes in Computer Science, pages 105–124. Springer-Verlag, 1986.
G. Grätzer. General Lattice Theory. Akademie-Verlag, Berlin, 1978.
L. A. Hemaspaandra, A. Hoene, A. V. Naik, M. Ogihara, A. L. Selman, T. Thierauf, and J. Wang. Nondeterministically selective sets. International Journal of Foundations of Computer Science, 6(4):403–416, 1995.
U. Hertrampf. Locally definable acceptance types — the three-valued case. In Proceedings 1st Latin American Symposium on Theoretical Informatics, volume 583 of Lecture Notes in Computer Science, pages 262–271, Berlin, 1992. Springer-Verlag.
J. Kadin. The polynomial time hierarchy collapses if the Boolean hierarchy collapses. SIAM Journal on Computing, 17(6):1263–1282, 1988. Erratum in same journal 20(2):404, 1991.
J. Köbler, U. Schöning, and K. W. Wagner. The difference and truth-table hierarchies for NP. RAIRO Theoretical Informatics and Applications, 21(4):419–435, 1987.
K. W. Wagner and G. Wechsung. On the boolean closure of NP. Extended abstract as: G. Wechsung. On the boolean closure of NP. Proceedings 5th International Conference on Fundamentals in Computation Theory, volume 199 of Lecture Notes in Computer Science, pages 485–493, Berlin, 1985.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Kosub, S., Wagner, K.W. (2000). The Boolean Hierarchy of NP-Partitions. In: Reichel, H., Tison, S. (eds) STACS 2000. STACS 2000. Lecture Notes in Computer Science, vol 1770. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46541-3_13
Download citation
DOI: https://doi.org/10.1007/3-540-46541-3_13
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-67141-1
Online ISBN: 978-3-540-46541-6
eBook Packages: Springer Book Archive