We give the first extension of the result due to Paul, Pippenger, Szemeredi and Trotter [24] that deterministic linear time is distinct from nondeterministic linear time. We show that N T IM E(n

Nepomnjaˇsčiǐ’s Theorem states that for all 0 ≤ ǫ < 1 and k> 0 the class of languages recognized in nondeterministic time n k and space n ǫ, NTISP[n k, n ǫ], 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 Nepomnjaˇsčiǐ’s result to give a subhierarchy, Eu-LinH, of the linear time hierarchy that is contained in NP and which contains NTISP[n k, n ǫ]. 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, ξ-LinH, is defined to reduce the space requirements needed for the upper bound on Eu-LinH. Mathematics Subject Classification: 03F30, 68Q15 Keywords: structural complexity, linear time hierarchy, Nepomnjaˇsčiǐ’s Theorem