Alternating Rebound Turing Machines

Lan ZHANG; Jianliang XU; Katsushi INOUE; Akira ITO; Yue WANG

Alternating Rebound Turing Machines

Lan ZHANG, Jianliang XU, Katsushi INOUE, Akira ITO, Yue WANG

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This paper introduces an alternating rebound Turing machine and investigates some fundamental properties of it. Let DRTM (NRTM,ARTM) denote a deterministic (nondeterministic and alternating) rebound Turing machine, and URTM denote an ARTM with only universal states. We first investigate a relationship between the accepting powers of rebound machines and ordinary machines, and show, for example, that (1) there exists a language accepted by a deterministic 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 counter 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 by alternating rebound automata, but not accepted by any o(logn) space-bounded 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 investigate a relationship between the strong and weak modes of space complexity, and finally show that the classes of languages accepted by o(logn) space-bounded DRTM's (NRTM's, URTM's) are not closed under concatenation and Kleene .

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E82-A No.5 pp.745-755

Publication Date: 1999/05/25

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Type of Manuscript: Special Section PAPER (Special Section on Discrete Mathematics and Its Applications)

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Lan ZHANG, Jianliang XU, Katsushi INOUE, Akira ITO, Yue WANG, "Alternating Rebound Turing Machines" in IEICE TRANSACTIONS on Fundamentals, vol. E82-A, no. 5, pp. 745-755, May 1999, doi: .
Abstract: This paper introduces an alternating rebound Turing machine and investigates some fundamental properties of it. Let DRTM (NRTM,ARTM) denote a deterministic (nondeterministic and alternating) rebound Turing machine, and URTM denote an ARTM with only universal states. We first investigate a relationship between the accepting powers of rebound machines and ordinary machines, and show, for example, that (1) there exists a language accepted by a deterministic 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 counter 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 by alternating rebound automata, but not accepted by any o(logn) space-bounded 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 investigate a relationship between the strong and weak modes of space complexity, and finally show that the classes of languages accepted by o(logn) space-bounded DRTM's (NRTM's, URTM's) are not closed under concatenation and Kleene .
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e82-a_5_745/_p

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@ARTICLE{e82-a_5_745,
author={Lan ZHANG, Jianliang XU, Katsushi INOUE, Akira ITO, Yue WANG, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Alternating Rebound Turing Machines},
year={1999},
volume={E82-A},
number={5},
pages={745-755},
abstract={This paper introduces an alternating rebound Turing machine and investigates some fundamental properties of it. Let DRTM (NRTM,ARTM) denote a deterministic (nondeterministic and alternating) rebound Turing machine, and URTM denote an ARTM with only universal states. We first investigate a relationship between the accepting powers of rebound machines and ordinary machines, and show, for example, that (1) there exists a language accepted by a deterministic 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 counter 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 by alternating rebound automata, but not accepted by any o(logn) space-bounded 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 investigate a relationship between the strong and weak modes of space complexity, and finally show that the classes of languages accepted by o(logn) space-bounded DRTM's (NRTM's, URTM's) are not closed under concatenation and Kleene .},
keywords={},
doi={},
ISSN={},
month={May},}

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TY - JOUR
TI - Alternating Rebound Turing Machines
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 745
EP - 755
AU - Lan ZHANG
AU - Jianliang XU
AU - Katsushi INOUE
AU - Akira ITO
AU - Yue WANG
PY - 1999
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E82-A
IS - 5
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - May 1999
AB - This paper introduces an alternating rebound Turing machine and investigates some fundamental properties of it. Let DRTM (NRTM,ARTM) denote a deterministic (nondeterministic and alternating) rebound Turing machine, and URTM denote an ARTM with only universal states. We first investigate a relationship between the accepting powers of rebound machines and ordinary machines, and show, for example, that (1) there exists a language accepted by a deterministic 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 counter 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 by alternating rebound automata, but not accepted by any o(logn) space-bounded 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 investigate a relationship between the strong and weak modes of space complexity, and finally show that the classes of languages accepted by o(logn) space-bounded DRTM's (NRTM's, URTM's) are not closed under concatenation and Kleene .
ER -