Nepomnjascii's Theorem states that for all 0 0 the
class of languages recognized in nondeterministic time n^k and space
n^\epsilon, NTISP[n^k, n^\epsilon ], is contained in the linear time hierarchy.
By considering restrictions on the size of the universal quantifiers in the
linear time hierarchy, this paper refines Nepomnjascii's result to give a sub-
hierarchy, Eu-LinH, of the linear time hierarchy that is contained in NP and
which contains NTISP[n^k, n^\epsilon ]. Hence, Eu-LinH contains NL and SC. This
paper investigates basic structural properties of Eu-LinH. Then the
relationships between Eu-LinH and the classes NL, SC, and NP are considered to
see if they can shed light on the NL = NP or SC = NP questions. Finally, a new
hierarchy, zeta -LinH, is defined to reduce the space requirements needed for
the upper bound on Eu-LinH.Comment: 14 page