Theory of one-tape linear-time Turing machines

  • Authors:

  • Kohtaro Tadaki;Tomoyuki Yamakami;Jack C. H. Lin

  • Affiliations:

  • ERATO Quantum Computation and Information Project, Japan Science and Technology Corporation, Tokyo, 113-0033, Japan;School of Information Technology and Engineering, University of Ottawa, Ottawa, Ontario, Canada, K1N 6N5;School of Information Technology and Engineering, University of Ottawa, Ottawa, Ontario, Canada, K1N 6N5

  • Venue:
  • Theoretical Computer Science
  • Year:
  • 2010

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Abstract

A theory of one-tape two-way one-head off-line linear-time Turing machines is essentially different from its polynomial-time counterpart since these machines are closely related to finite state automata. This paper discusses structural-complexity issues of one-tape Turing machines of various types (deterministic, nondeterministic, reversible, alternating, probabilistic, counting, and quantum Turing machines) that halt in linear time, where the running time of a machine is defined as the length of any longest computation path. We explore structural properties of one-tape linear-time Turing machines and clarify how the machines' resources affect their computational patterns and power.