This paper introduces an alternating rebound Turing machine and investigate
s some fundamental properties of it. Let DRTM (NRTM,ARTM) denote a determin
istic (nondeterministic and alternating) rebound Turing machine, and URTM d
enote an ARTM with only universal states. We first investigate a relationsh
ip between the accepting powers of rebound machines and ordinary machines,
and show, for example, that (1) there exists a language accepted by a deter
ministic rebound automaton, but not accepted by any o(log n) space-bounded
alternating Turing machine, (2) alternating rebound automata are equivalent
to two-way alternating counter automata, and (3) deterministic rebound cou
nter automata are more powerful than two-way deterministic counter automata
. We next investigate a relationship among the accepting powers of DRTM's,
NRTM's, URTM's and ARTM's, and show that there exists a language accepted b
y alternating rebound automata, but not accepted by any o(log n) space-boun
ded NRTM (URTM). Then we show that there exists an infinite space hierarchy
for DRTM's (NRTM's, URTM's) with spaces below log n. Furthermore, we inves
tigate a relationship between the strong and weak modes of space complexity
, and finally show that the classes of languages accepted by o(log n) space
-bounded DRTM's (NRTM's, URTM's) are not closed under concatenation and Kle
ene +.