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.
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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.
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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
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DOI: https://doi.org/10.1007/3-540-46541-3_13
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