Measures of parallelism in alternating computation trees (Extended Abstract)

King, K. N.

doi:10.1145/800076.802472

Cited by 6 publications

(3 citation statements)

References 4 publications

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“…The dual result for nondeterministic AuxPDA (with also preservation of the polynomial running-time) could be shown earlier by Ruzzo [Ruz80]. This result can be generalized: s(n) space and r(n) reversal bounded nondeterministic AuxPDA can be simulated within same space and reversal bounds and with a pushdown height bounded by O(s(n) 1 log(r(n))) [Kin81,BH89]. Herein, the reversal bound refers to the restriction of the number of pushdown reversals.…”

Section: Other Applicationsmentioning

confidence: 66%

Unambiguous simulations of auxiliary pushdown automata and circuits

Niedermeier

Rossmanith

1992

Latin '92

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In this paper time-bounded auxiliary push-down automata (AuxPDA), i.e. time and space bounded Turing machines with additional pushdown store, are considered. We investigate the power of unambiguous AuxPDA, i.e., machines that have at most one accepting computation, and ambiguity bounded AuxPDA.Recently, it was shown by Buntrock, Hemachandra, and Siefkes that space bounded Turing machines, whose computation trees have moderate ambiguity, can be eciently simulated by unambiguous AuxPDA with same space bound. This paper shows that such an ecient simulation is also possible for AuxPDA. The simulation incorporates no space and time penalty, unless the ambiguity is very high.By similar methods it is shown that unambiguous AuxPDA can eciently simulate a certain class of unambiguous, semi-unbounded fan-in circuits, which answers an open question posed by Lange.Finally, obliviousness for AuxPDA is considered and it is proved that unambiguous Aux-PDA work w.l.o.g. with a very limited amount of space on the pushdown store, a result that is already known for deterministic and nondeterministic AuxPDA.

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Section: Other Applicationsmentioning

confidence: 66%

Unambiguous simulations of auxiliary pushdown automata and circuits

Niedermeier

Rossmanith

1992

Latin '92

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“…(Recently [15], K.N.King introduced the safe cor~olexity measure as "leaf-size" independently. In [15], the term "branching" is adopted instead of the term "leaf-size". ) Basically We need the following three definitions for the next theor~n.…”

Section: Leaf-size Bounded Alternationmentioning

confidence: 99%

Two-dimensional alternating Turing machines

Inoue

Takanami

Taniguchi

1982

Proceedings of the Fourteenth Annual ACM Symposium on Theory of Computing - STOC '82

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This paper introduces a two-dimensional alternating Turing machine (2-ATM) which is an extension of an alternating Turing machine to twodimensions. This paper also introduces a three-way two-dimensional alternating Turing machine (TR2-ATM ) which is an alternating version of a three-way two-dimensional Turing machine. We first investigate a relationship between the accepting powers of space-bounded 2-ATM's (or TR2-ATM's) and ordinary space-bounded two-d~sional Turing machines (or three-way two-d~sional Turing machines). We then introduce a siaple, natural complexity measure for 2-ATM's (or TR2-ATM's), called "leaf-size", and provides a spectrum of cc~plexity classes based on leaf-size bounded cc~putations. We finally investigate the recognizability of connected patterns by 2-ATM's (or TR2-ATM's). i. IntroductionDuring the past ten years, many autc~ata on a twodimensional tape have been introduced, and several properties of them have been given [1][2][3][4][5][6][7][8][9]. Recently, (one-dimensional) alternating Turing machines were introduced in [i0] as a generalization of nondeterministic Turing machines and as a mechanis~n to model parallel ccaputation. In papers [11-15], several investigations of alternating machines have been continued. It seems to us, however, that there are many problems about alternating machines to be solved in the future. This paper intmoduces a two-dimensional alternating Turing machine (2-ATM) which is an alternating version of a two-dimensional Turing machine (TM) [ 3,6,7]. That is, a 2-ATM is a TM whose states are Permission to copy without fee all or part of this material is granted provided that the copies are not made or distributed for direct commercial advantage, the ACM copyright notice and the title of the publication and its date appear, and notice is given that copying is by permission of the Association for Computing Machinery. To copy otherwise, or to republish, requires a fee and/or specific permission. © 1982 ACMO-89791-067-2/82/O05/O037 $00.75 partitioned into "existential" and "universal" states, like one-dimensional alternating Turing machines. This paper also introduces a three-way twodimensional alternating Turing machine (TR2-ATM) which is an alternating version of three-way twodimensional Turing machine (TRTM) [7]. The main purpose of this paper is to get the deeper under-

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“…Regarding other related work, other authors, including Gurari and Ibarra [8], King [13], and Ruzzo [17] give relationships between alternating Turing machines on the one hand and deterministic or nondeterministic auxiliary pushdown or stack automata on the other. However, these papers do not consider alternating auxiliary pushdown or stack automata.…”

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confidence: 99%