### 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, 0<α<1, there is a deterministic time function T=ω(n^{2}) such that T^{α} is not equivalent to any time function of a deterministic turing machine.

Original language | English (US) |
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Pages (from-to) | 295-299 |

Number of pages | 5 |

Journal | Theory of Computing Systems |

Volume | 36 |

Issue number | 3 |

DOIs | |

State | Published - May 1 2003 |

Externally published | Yes |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computational Theory and Mathematics

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## Cite this

Lipton, R. J., Ogihara, M., & Zalcstein, Y. (2003). A note on square rooting of time functions of turing machines.

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