A note on one-pebble two-dimensional Turing machines

Authors:
Atsuyuki Inoue;Katsushi Inoue;Akira Ito;Yue Wang;Tokio Okazaki
Affiliations:
Department of Computer Science and Systems Engineering, Faculty of Engineering, Yamaguchi University, Uhe, Yamaguchi 755-8611, Japan;Department of Computer Science and Systems Engineering, Faculty of Engineering, Yamaguchi University, Uhe, Yamaguchi 755-8611, Japan;Department of Computer Science and Systems Engineering, Faculty of Engineering, Yamaguchi University, Uhe, Yamaguchi 755-8611, Japan;Department of Computer Science and Systems Engineering, Faculty of Engineering, Yamaguchi University, Uhe, Yamaguchi 755-8611, Japan;Department of Media and Culture Studies, Faculty of Humanities, Josai International University, Togane, China 283-8555, Japan
Venue:
Information Sciences: an International Journal
Year:
2004

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Abstract

This paper investigates a relationship among the accepting powers of deterministic, nondeterministic, and alternating one-pebble two-dimensional Turing machines, and shows that 1. nondeterminism are more powerful than determinism for o(log n) space-bounded one-pebble two-dimensional Turing machines whose input tapes are restricted to square ones, and 2. alternation are more powerful than nondeterminism for f(m) + g(n) (resp., f(m) × g(n)) space-bounded one-pebble two-dimensional Turing machines, where f : N → N is an arbitrary monotonic nondecreasing function space-constructible by a deterministic one-pebble two-dimensional Turing machine, and g : N → N is an arbitrary function such that g(n) = o(log n) (resp., g(n) = o(log n/log logn)).