小字母表上双向确定性有限自动机的单向确定性模拟

IF 0.6 4区 计算机科学 Q4 COMPUTER SCIENCE, THEORY & METHODS
V. Geffert, Alexander Okhotin
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引用次数: 0

摘要

研究表明,一个在字母表[公式:见正文]上具有[公式:见正文]状态的双向确定性有限自动机(2DFA)可以转化为具有[公式:见正文]状态的等效单向自动机(1DFA),其中[公式:见正文]。这反映了这样一个事实,即通过在内存中保留最后处理过的符号[公式:见文本],模拟的 1DFA 可以记住[公式:见文本]状态中的一种,在这种状态下,自动机通过[公式:见文本]向右移动,并记住一个将向左移动的[公式:见文本]状态映射为向右移动的[公式:见文本]状态的函数;参见经典结构中的[公式:见文本]函数。使用 2 符号字母表建立了[公式:见正文]状态的接近下限,见证语言由方向确定的 2DFA 定义。用扫频 2DFA 定义的见证语言也能达到同样的下限,但需要使用 5 个符号的字母表。此外,将扫频或方向决定型 2DFA 转换为 1DFA 的复杂度恰好为[公式:见正文]。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Deterministic One-Way Simulation of Two-Way Deterministic Finite Automata Over Small Alphabets
It is shown that a two-way deterministic finite automaton (2DFA) with [Formula: see text] states over an alphabet [Formula: see text] can be transformed to an equivalent one-way automaton (1DFA) with [Formula: see text] states, where [Formula: see text]. This reflects the fact that, by keeping the last processed symbol [Formula: see text] in memory, the simulating 1DFA can remember one of [Formula: see text] states in which the automaton moves by [Formula: see text] to the right, and a function that maps [Formula: see text] states moving to the left to [Formula: see text] states moving to the right; cf. ca. [Formula: see text] functions in the classical construction. A close lower bound of [Formula: see text] states is established using a 2-symbol alphabet, with witness languages defined by direction-determinate 2DFA. The same lower bound is also achieved with witness languages defined by sweeping 2DFA, at the expense of using a 5-symbol alphabet. In addition, the complexity of transforming a sweeping or a direction-determinate 2DFA to a 1DFA is shown to be exactly [Formula: see text].
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来源期刊
International Journal of Foundations of Computer Science
International Journal of Foundations of Computer Science 工程技术-计算机:理论方法
CiteScore
1.60
自引率
12.50%
发文量
63
审稿时长
3 months
期刊介绍: The International Journal of Foundations of Computer Science is a bimonthly journal that publishes articles which contribute new theoretical results in all areas of the foundations of computer science. The theoretical and mathematical aspects covered include: - Algebraic theory of computing and formal systems - Algorithm and system implementation issues - Approximation, probabilistic, and randomized algorithms - Automata and formal languages - Automated deduction - Combinatorics and graph theory - Complexity theory - Computational biology and bioinformatics - Cryptography - Database theory - Data structures - Design and analysis of algorithms - DNA computing - Foundations of computer security - Foundations of high-performance computing
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