可逆有限自动机

IF 0.4 4区 计算机科学 Q4 COMPUTER SCIENCE, SOFTWARE ENGINEERING Fundamenta Informaticae Pub Date : 2015-09-09 DOI:10.3233/FI-2017-1575
Martin Kutrib, Matthias Wendlandt
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引用次数: 15

摘要

有限k自动机是一种线性有界自动机,它只能在前k次访问中重写每个磁带方,其中\(k\ge 0\)是一个固定常数。众所周知,这些自动机只接受与上下文无关的语言。我们研究了确定性k限制自动机执行可逆计算的能力,即每个构型最多有一个前驱的计算。第一个结果是,对于所有\(k\ge 0\),扫描限制k的自动机只接受常规语言。与可逆有限自动机相比,所有正则语言都可以被扫描0限制自动机所接受。然后我们研究了k次可能的重写操作所获得的计算能力。证明了可逆的2-限制自动机只接受正则语言,因此它比一般的2-限制自动机严格弱。此外,还得到了可逆3限和4限自动机语言之间的适当包含。层次结构的下一层在每个k和\(k+3\)重写操作之间分开。最后,事实证明,所有k有限自动机都只接受Church-Rosser语言,也就是说,上下文无关语言和Church-Rosser语言之间的交集包含了超越确定性上下文无关语言的语言族的无限层次结构。
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Reversible Limited Automata
A k-limited automaton is a linear bounded automaton that may rewrite each tape square only in the first k visits, where \(k\ge 0\) is a fixed constant. It is known that these automata accept context-free languages only. We investigate deterministic k-limited automata towards their ability to perform reversible computations, that is, computations in which every configuration has at most one predecessor. A first result is that, for all \(k\ge 0\), sweeping k-limited automata accept regular languages only. In contrast to reversible finite automata, all regular languages are accepted by sweeping 0-limited automata. Then we study the computational power gained in the number k of possible rewrite operations. It is shown that the reversible 2-limited automata accept regular languages only and, thus, are strictly weaker than general 2-limited automata. Furthermore, a proper inclusion between reversible 3-limited and 4-limited automata languages is obtained. The next levels of the hierarchy are separated between every k and \(k+3\) rewrite operations. Finally, it turns out that all k-limited automata accept Church-Rosser languages only, that is, the intersection between context-free and Church-Rosser languages contains an infinite hierarchy of language families beyond the deterministic context-free languages.
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来源期刊
Fundamenta Informaticae
Fundamenta Informaticae 工程技术-计算机:软件工程
CiteScore
2.00
自引率
0.00%
发文量
61
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.
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