doi:10.1016/j.tcs.2005.04.003 
Copyright © 2005 Elsevier B.V. All rights reserved.
Some properties of one-pebble Turing machines with sublogarithmic space
aDepartment of Computer Science and Systems Engineering, Faculty of Engineering, Yamaguchi University, Ube, Yamaguchi 755-8611, Japan
bDepartment of Media and Culture Studies, Faculty of Humanities, Josai International University, Togane, Chiba 283-8555, Japan
Received 16 September 2003;
accepted 18 April 2005.
Communicated by M. Ito.
Available online 17 May 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 
and 
. 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 
space-bounded alternating one-pebble Turing machine, but not accepted by any weakly 
space-bounded nondeterministic one-pebble Turing machine. Finally, we investigate a space hierarchy, and show that for any one-pebble (fully) space constructible function 
, 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.
Keywords: Deterministic one-counter automata; One-pebble Turing machines; Alternation; Space hierarchy
Abstract
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