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arXiv · 0801.1307

Alternating Hierarchies for Time-Space Tradeoffs

Chris Pollett·Eric Miles
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Abstract

Nepomnjascii's Theorem states that for all 0 <= ε< 1 and k > 0 the class of languages recognized in nondeterministic time n^k and space n^ε, NTISP[n^k, n^ε], 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^ε]. 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.

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Chris Pollett, Eric Miles. 2008-01-08. Alternating Hierarchies for Time-Space Tradeoffs. https://arxiv.org/abs/0801.1307

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