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On Separators, Segregators and Time versus Space
"... 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 ..."
Abstract

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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
Abstract
, 2008
"... 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, ..."
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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, EuLinH, of the linear time hierarchy that is contained in NP and which contains NTISP[n k, n ǫ]. Hence, EuLinH contains NL and SC. This paper investigates basic structural properties of EuLinH. Then the relationships between EuLinH 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, ξLinH, is defined to reduce the space requirements needed for the upper bound on EuLinH. Mathematics Subject Classification: 03F30, 68Q15 Keywords: structural complexity, linear time hierarchy, Nepomnjaˇsčiǐ’s Theorem