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Simulating Two Pushdown Stores by One Tape in $O(n^{1.5}\sqrt{logn}$) Time. (Preliminary Version)

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Based on two graph separator theorems, one old (the Lipton-Tarjan planar separator theorem) and one new, we present two unexpected upper bounds and resolve several open problems for on-line computations: (1) 1 tape nondeterministic machines can simulate 2 pushdown stores in time O(n1.5logn) (true for both on-line and off-line machines). Together with the Ω(n1.5logn) lower bound by the author [L1], this solved the open problem 1 in [DGPR] for the 1 tape vs. 2 pushdown case. It also disproves the commonly conjectured Ω(n2) lower bound. (Note, the Ω(n2) lower bound has been proved for the deterministic case [M, L, V].) (2) the languages defined by [M] and [F], aimed to obtain optimal lower bound for 1 tape nondeterministic machines, can be accepted in O(n2loglogn/logn) and O(n1.5logn) time by a 1 tape TM, respectively. (3) 3 pushdown stores are better than 2 pushdown stores. This answers open problem 3 of [DG]. (An Ω(n4/3/logen) lower bound is also obtained.) (4) 1 tape can nondeterministically simulate 1 queue in O(n1.5logn) time. (The lower bounds were: Ω(n2) for deterministic case [V] and Ω(n4/3/logn) [L1] for nondeterministic case.)

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1985-03

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Cornell University

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computer science; technical report

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http://techreports.library.cornell.edu:8081/Dienst/UI/1.0/Display/cul.cs/TR85-667

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technical report

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