Nondeterministic one-tape off-line turing machines and their time complexity

  • Authors:

  • Giovanni Pighizzini

  • Affiliations:

  • Dipartimento di Informatica e Comunicazione, Università degli Studi di Milano, Milano, Italy

  • Venue:
  • Journal of Automata, Languages and Combinatorics
  • Year:
  • 2009

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Abstract

In this paper we consider the time and the crossing sequence complexities of one-tape off-line Turing machines. We show that the running time of each nondeterministic machine accepting a nonregular language must grow at least as n log n, in the case all accepting computations are considered (accept measure). We also prove that the maximal length of the crossing sequences used in accepting computations must grow at least as log n. On the other hand, it is known that if the time is measured considering, for each accepted string, only the faster accepting computation (weak measure), then there exist nonregular languages accepted in linear time. We prove that under this measure, each accepting computation should exhibit a crossing sequence of length at least log log n. We also present efficient implementations of algorithms accepting some unary nonregular languages.