A note on square rooting of time functions of turing machines

Richard J. Lipton, Mitsunori Ogihara, Yechezkel Zalcstein

Research output: Contribution to journalArticle


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.

Original languageEnglish (US)
Pages (from-to)295-299
Number of pages5
JournalTheory of Computing Systems
Issue number3
StatePublished - May 1 2003


ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computational Theory and Mathematics

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