Alternating Hierarchies for Time-Space Tradeoffs

Nepomnjascii's Theorem states that for all 0 < 1 and k > 0 the class of languages recognized in nondeterministic time nk and space n , NTISP[nk , n ], 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 subhierarchy, Eu-LinH, of the linear time hierarchy that is contained in NP and which contains NTISP[nk , n ]. 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, -LinH, is defined to reduce the space requirements needed for the upper bound on Eu-LinH. Mathematics Subject Classification: 03F30, 68Q15

• Type: Journal
• Year: 2008
• Where: CORR
• Authors: Chris Pollett, Eric Miles
• Keywords: CORR 2008, Education, Linear Time, Nondeterministic Time Nk, Time Hierarchy