Between SC and LOGDCFL: families of languages accepted by logarithmic-space deterministic auxiliary depth-k storage automata

IF 0.9 Q3 COMPUTER SCIENCE, THEORY & METHODS
T. Yamakami
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引用次数: 0

Abstract

The closure of deterministic context-free languages under logarithmic-space many-one reductions ( -m-reductions), known as LOGDCFL, has been studied in depth from an aspect of parallel computability because it is nicely situated between and . By replacing a memory device of pushdown automata with an access-controlled storage tape, we introduce a computational model of one-way deterministic depth-k storage automata (k-sda's) whose tape cells are freely modified during the first k accesses and then become blank forever. These k-sda's naturally induce the language family . Similarly to , we study the closure of all languages in under -m-reductions. We demonstrate that by significantly extending Cook's early result (1979) of . The entire hierarch of for all therefore lies between and . As an immediate consequence, we obtain the same simulation bounds for Hibbard's limited automata. We further characterize in terms of a new machine model, called logarithmic-space deterministic auxiliary depth-k storage automata that run in polynomial time. These machines are as powerful as a polynomial-time two-way multi-head deterministic depth-k storage automata. We also provide a ‘generic’ -complete language under -m-reductions by constructing a two-way universal simulator working for all k-sda's.
SC与LOGDCFL之间:对数空间确定性辅助深度k存储自动机所接受的语言族
确定性上下文无关语言在对数空间多一约简(-m-约简)下的闭包,即LOGDCFL,已经从并行可计算性的角度进行了深入研究,因为它很好地位于和之间。通过用访问控制的存储磁带代替下推自动机的存储设备,我们引入了一种单向确定性深度k存储自动机(k-sda)的计算模型,该自动机的磁带单元在前k次访问期间被自由修改,然后永远变为空白。这些k-sda很自然地引出了语族。类似地,我们研究所有语言在-m-约简下的闭包。我们通过显著扩展Cook的早期结果(1979)来证明这一点。因此,“为所有人”的整个等级介于和之间。作为直接的结果,我们得到了Hibbard有限自动机的相同的模拟边界。我们进一步描述了一种新的机器模型,称为对数空间确定性辅助深度k存储自动机,它在多项式时间内运行。这些机器与多项式时间双向多头确定性深度k存储自动机一样强大。我们还通过构建一个适用于所有k-sda的双向通用模拟器,提供了一个在-m-约简下的“通用”完备语言。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
International Journal of Computer Mathematics: Computer Systems Theory
International Journal of Computer Mathematics: Computer Systems Theory Computer Science-Computational Theory and Mathematics
CiteScore
1.80
自引率
0.00%
发文量
11
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