Hierarchical Unambiguity

Details Hierarchical Unambiguity Hierarchical Unambiguity

2007-02-08

arxiv.org/abs/cs/0702047v1

Computer Science

Computational Complexity

Scientific paper

We develop techniques to investigate relativized hierarchical unambiguous computation. We apply our techniques to generalize known constructs involving relativized unambiguity based complexity classes (UP and \mathcal{UP}) to new constructs involving arbitrary higher levels of the relativized unambiguous polynomial hierarchy (UPH). Our techniques are developed on constraints imposed by hierarchical arrangement of unambiguous nondeterministic polynomial-time Turing machines, and so they differ substantially, in applicability and in nature, from standard methods (such as the switching lemma [Hastad, Computational Limitations of Small-Depth Circuits, MIT Press, 1987]), which play roles in carrying out similar generalizations. Aside from achieving these generalizations, we resolve a question posed by Cai, Hemachandra, and Vyskoc [J. Cai, L. Hemachandra, and J. Vyskoc, Promises and fault-tolerant database access, In K. Ambos-Spies, S. Homer, and U. Schoening, editors, Complexity Theory, pages 101-146. Cambridge University Press, 1993] on an issue related to nonadaptive Turing access to UP and adaptive smart Turing access to \mathcal{UP}.

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