The Boolean Hierarchy of NP-Partitions
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.
KeywordsEquivalence Class Partial Order Boolean Function Partition Class Acceptance Type
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- 2.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.Google Scholar
- 3.G. Grätzer. General Lattice Theory. Akademie-Verlag, Berlin, 1978.Google Scholar
- 5.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.Google Scholar
- 8.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.Google Scholar