Some properties of one-pebble turing machines with sublogarithmic space

  • Authors:

  • Atsuyuki Inoue;Akira Ito;Katsushi Inoue;Tokio Okazaki

  • Affiliations:

  • Department of Computer Science and Systems Engineering, Faculty of Engineering, Yamaguchi University, Ube, Yamaguchi, Japan;Department of Computer Science and Systems Engineering, Faculty of Engineering, Yamaguchi University, Ube, Yamaguchi, Japan;Department of Computer Science and Systems Engineering, Faculty of Engineering, Yamaguchi University, Ube, Yamaguchi, Japan;Department of Media and Culture Studies, Faculty of Humanities, Josai International University, Togane, Japan

  • Venue:
  • Theoretical Computer Science
  • Year:
  • 2005

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Abstract

This paper investigates some aspects of the accepting powers of deterministic, nondeterministic, and alternating one-pebble Turing machines with spaces between log log n and log n. We first investigate a relationship between the accepting powers of two-way deterministic one-counter automata and deterministic (or nondeterministic) one-pebble Turing machines, and show that they are incomparable. Then we investigate a relationship between nondeterminism and alternation, and show that there exists a language accepted by a strongly log log n space-bounded alternating one-pebble Turing machine, but not accepted by any weakly o(log n) space-bounded nondeterministic one-pebble Turing machine. Finally, we investigate a space hierarchy, and show that for any one-pebble (fully) space constructible function L(n) ≤ log n, and for any function L'(n) = o(L(n)), there exists a language accepted by a strongly L(n) space-bounded deterministic one-pebble Turing machine, but not accepted by any weakly L'(n) space-bounded nondeterministic one-pebble Turing machine.