Deterministic One-Way Turing Machines with Sublinear Space

IF 0.4 4区计算机科学 Q4 COMPUTER SCIENCE, SOFTWARE ENGINEERING

Fundamenta Informaticae Pub Date : 2013-08-13 DOI:10.3233/FI-2015-1147

Martin Kutrib, Julien Provillard, György Vaszil, Matthias Wendlandt

引用次数: 7

Abstract

Deterministic one-way Turing machines with sublinear space bounds are systematically studied. We distinguish among the notions of strong, weak, and restricted space bounds. The latter is motivated by the study of P automata. The space available on the work tape depends on the number of input symbols read so far, instead of the entire input. The class of functions space constructible by such machines is investigated, and it is shown that every function f that is space constructible by a deterministic two-way Turing machine, is space constructible by a strongly f space-bounded deterministic one-way Turing machine as well. We prove that the restricted mode coincides with the strong mode for space constructible functions. The known infinite, dense, and strict hierarchy of strong space complexity classes is derived also for the weak mode by Kolmogorov complexity arguments. Finally, closure properties under AFL operations, Boolean operations and reversal are shown.

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具有次线性空间的确定性单向图灵机

系统地研究了具有次线性空间界的确定性单向图灵机。我们区分了强、弱和受限空间界限的概念。后者的动机是对P自动机的研究。工作磁带上的可用空间取决于到目前为止读取的输入符号的数量，而不是整个输入。研究了在这种机器上空间可构造的函数类，证明了在确定性双向图灵机上空间可构造的函数f，在强空间有界的确定性单向图灵机上也是空间可构造的。证明了空间可构造函数的约束模态与强模态重合。已知的无限的、密集的、严格的强空间复杂度类的层次结构也通过Kolmogorov复杂度参数为弱模导出。最后，给出了AFL操作、布尔操作和反转操作下的闭包性质。

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

Fundamenta Informaticae 工程技术-计算机：软件工程

CiteScore

2.00

自引率

0.00%

发文量

审稿时长

9.8 months

期刊介绍： Fundamenta Informaticae is an international journal publishing original research results in all areas of theoretical computer science. Papers are encouraged contributing: solutions by mathematical methods of problems emerging in computer science solutions of mathematical problems inspired by computer science. Topics of interest include (but are not restricted to): theory of computing, complexity theory, algorithms and data structures, computational aspects of combinatorics and graph theory, programming language theory, theoretical aspects of programming languages, computer-aided verification, computer science logic, database theory, logic programming, automated deduction, formal languages and automata theory, concurrency and distributed computing, cryptography and security, theoretical issues in artificial intelligence, machine learning, pattern recognition, algorithmic game theory, bioinformatics and computational biology, quantum computing, probabilistic methods, algebraic and categorical methods.