部分词自动机问题的计算复杂度

IF 0.4 4区 计算机科学 Q4 COMPUTER SCIENCE, SOFTWARE ENGINEERING
M. Holzer, Sebastian Jakobi, Matthias Wendlandt
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引用次数: 5

摘要

我们考虑了部分词自动机相关问题的计算复杂性。粗略地说,部分词是其中某些位置未指定的词,而部分词自动机是接受部分词语言的有限自动机——在这里,单词中未指定的位置由一个“孔”符号表示。部分单词语言L可以通过使用-替换转换为普通语言L。特别地,我们研究了部分词自动机的压缩或最小化问题的复杂性,这是已知的np困难。通过展示PSPACE-completeness,我们改进了先前已知的这个问题的复杂性。事实上,事实证明,几乎所有与部分词自动机相关的问题,例如,等价性和普遍性,已经是pspace完全的。此外,我们还在所涉及的自动机只接受有限语言的进一步限制下研究了这些问题。在这种情况下,所研究问题的复杂性随所研究的问题的不同而从pspace -完全性下降到conp -硬度和§P中的包容。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
On the Computational Complexity of Partial Word Automata Problems
We consider computational complexity of problems related to partial word au- tomata. Roughly speaking, a partial word is a word in which some positions are unspecified, and a partial word automaton is a finite automaton that accepts a partial word language— here the unspecified positions in the word are represented by a "hole" symbol ⋄. A partial word language Lcan be transformed into an ordinary language L by using a ⋄-substitution. In particular, we investigate the complexity of the compression or minimization problem for partial word automata, which is known to be NP-hard. We improve on the previously known complexity on this problem, by showing PSPACE-completeness. In fact, it turns out that almost all problems related to partial word automata, such as, e.g., equivalence and universality, are already PSPACE-complete. Moreover, we also study these problems under the further restriction that the involved automata accept only finite languages. In this case, the complexity of the studied problems drop from PSPACE-completeness down to coNP-hardness and containment in § P depending on the problem investigated.
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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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