TY - JOUR

T1 - A note on square rooting of time functions of turing machines

AU - Lipton, Richard J.

AU - Ogihara, Mitsunori

AU - Zalcstein, Yechezkel

N1 - Funding Information:
∗ The first and third authors were supported, in part, by NSF Grant CCR-0002299. The second author was supported, in part, by NSF Grants CCR-9701911, CCR-9725021, DUE-9980943, INT-9726724, NIH/NIA Grant RO1-AG18231, and DARPA Grant F30602-98-2-013.

PY - 2003/5

Y1 - 2003/5

N2 - Square rooting of time functions of turing machines was studied and analysed. The conjecture that for all nondeterministic time functions T that are ω(n2) the square root of T is equivalent to the time function of a nondeterministic turing machine. It was found that for every rational number α, 0<α<1, there is a deterministic time function T=ω(n2) such that Tα is not equivalent to any time function of a deterministic turing machine.

AB - Square rooting of time functions of turing machines was studied and analysed. The conjecture that for all nondeterministic time functions T that are ω(n2) the square root of T is equivalent to the time function of a nondeterministic turing machine. It was found that for every rational number α, 0<α<1, there is a deterministic time function T=ω(n2) such that Tα is not equivalent to any time function of a deterministic turing machine.

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U2 - 10.1007/s00224-002-1079-x

DO - 10.1007/s00224-002-1079-x

M3 - Article

AN - SCOPUS:0038269018

VL - 36

SP - 295

EP - 299

JO - Theory of Computing Systems

JF - Theory of Computing Systems

SN - 1432-4350

IS - 3

ER -