  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}.
