Hierarchical Unambiguity

Abstract. We develop techniques to investigate relativized hierarchical unambiguous computation. We apply our techniques to push forward some known constructs involving relativized unambiguity based complexity classes (UP and Promise-UP) to new constructs involving arbitrary levels of the relativized unambiguous polynomial hierarchy (UPH). Our techniques are developed on constraints imposed by hierarchical assembly of unambiguous nondeterministic polynomial-time Turing machines, and so our techniques differ substantially, in applicability and in nature, from standard techniques (such as the switching lemma [H˚as87]), which are known to play roles in carrying out similar generalizations. Aside from achieving these generalizations, we resolve a question posed by Cai, Hemachandra, and Vyskoˇc [CHV93] on an issue related to nonadaptive Turing access to UP and adaptive smart Turing access to Promise-UP.

• Type: Journal
• Year: 2007
• Where: CORR
• Authors: Holger Spakowski, Rahul Tripathi
• Keywords: CORR 2007, Education, Hierarchical Unambiguous Computation, Unambiguous, Unambiguous Nondeterministic Polynomial-time