Sharply Bounded Alternation and Quasilinear Time

We de ne the sharply bounded hierarchy, SBH(QL), a hierarchy of classes within P, using quasilinear-time computation and quanti cation over strings of length logn. It generalizes the limited nondeterminism hierarchy introduced by Buss and Goldsmith, while retaining the invariance properties. The new hierarchy has several alternative characterizations. We de ne both SBH(QL) and its corresponding hierarchy of function classes, and present a variety of problems in these classes, including ql m-complete problems for each class in SBH(QL). We discuss the structure of the hierarchy, and show that determining its precise relationship to deterministic time classes can imply P 6= PSPACE. We present characterizations of SBH(QL) relations based on alternating Turing machines and on rst-order de nability, as well as recursion-theoretic characterizations of function classes corresponding to SBH(QL). AMS(MOS) Subject Classi cations: 68Q15, 68Q05, 03D55, 03C13. Key Words: nondeterminism, quasilinear...

• Type: Journal
• Year: 1998
• Where: MST
• Authors: Stephen A. Bloch, Jonathan F. Buss, Judy Goldsmith
• Keywords: Characterizations, Function Classes, Limited Nondeterminism Hierarchy, MST 1998