### Abstract

Square rooting of time functions of turing machines was studied and analysed. The conjecture that for all nondeterministic time functions T that are ω(n^{2}) 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, 02) such that T^{α} is not equivalent to any time function of a deterministic turing machine.

Original language | English (US) |
---|---|

Pages (from-to) | 295-299 |

Number of pages | 5 |

Journal | Theory of Computing Systems |

Volume | 36 |

Issue number | 3 |

DOIs | |

State | Published - May 2003 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Theoretical Computer Science
- Computational Theory and Mathematics
- Mathematics(all)

### Cite this

*Theory of Computing Systems*,

*36*(3), 295-299. https://doi.org/10.1007/s00224-002-1079-x

**A note on square rooting of time functions of turing machines.** / Lipton, Richard J.; Ogihara, Mitsunori; Zalcstein, Yechezkel.

Research output: Contribution to journal › Article

*Theory of Computing Systems*, vol. 36, no. 3, pp. 295-299. https://doi.org/10.1007/s00224-002-1079-x

}

TY - JOUR

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

AU - Lipton, Richard J.

AU - Ogihara, Mitsunori

AU - Zalcstein, Yechezkel

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, 02) 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, 02) such that Tα is not equivalent to any time function of a deterministic turing machine.

UR - http://www.scopus.com/inward/record.url?scp=0038269018&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0038269018&partnerID=8YFLogxK

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 -