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The Word Problem for Finitary Automaton Groups 有限自动机群的字问题
Pub Date : 2023-02-21 DOI: 10.48550/arXiv.2302.10670
Maximilian Kotowsky, Jan Philipp Wächter
A finitary automaton group is a group generated by an invertible, deterministic finite-state letter-to-letter transducer whose only cycles are self-loops at an identity state. We show that, for this presentation of finite groups, the uniform word problem is coNP-complete. Here, the input consists of a finitary automaton together with a finite state sequence and the question is whether the sequence acts trivially on all input words. Additionally, we also show that the respective compressed word problem, where the state sequence is given as a straight-line program, is PSPACE-complete. In both cases, we give a direct reduction from the satisfiablity problem for (quantified) boolean formulae.
有限自动机群是由可逆的、确定性的有限状态字母到字母的换能器产生的群,其唯一周期是在恒等状态下的自环。我们证明,对于有限群的这种表示,一致字问题是conp完全的。这里,输入由有限自动机和有限状态序列组成,问题是该序列是否对所有输入单词都起作用。此外,我们还证明了相应的压缩词问题是pspace完备的,其中状态序列是作为直线程序给出的。在这两种情况下,我们给出了(量化)布尔公式的可满足性问题的直接简化。
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引用次数: 0
Ranking Binary Unlabelled Necklaces in Polynomial Time 排序二进制未标记项链在多项式时间
Pub Date : 2022-05-27 DOI: 10.48550/arXiv.2205.13916
Duncan Adamson
Unlabelled Necklaces are an equivalence class of cyclic words under both the rotation (cyclic shift) and the relabelling operations. The relabelling of a word is a bijective mapping from the alphabet to itself. The main result of the paper is the first polynomial-time algorithm for ranking unlabelled necklaces of a binary alphabet. The time-complexity of the algorithm is O ( n 6 log 2 n ), where n is the length of the considered necklaces. The key part of the algorithm is to compute the rank of any word with respect to the set of unlabelled necklaces by finding three other ranks: the rank over all necklaces, the rank over symmetric unlabelled necklaces, and the rank over necklaces with an enclosing labelling. The last two concepts are introduced in this paper.
在旋转(循环移位)和重新标记操作下,无标签项链是循环单词的等价类。一个单词的重新标记是一个从字母表到自身的双向映射。本文的主要成果是第一个用于排序二元字母表中未标记项链的多项式时间算法。该算法的时间复杂度为O (n 6 log 2 n),其中n是所考虑的项链的长度。该算法的关键部分是通过查找其他三个秩来计算任何单词相对于未标记项链集的秩:所有项链的秩,对称未标记项链的秩,以及带有封闭标签的项链的秩。本文介绍了后两个概念。
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引用次数: 4
Construction of a Bi-infinite Power Free Word with a Given Factor and a Non-recurrent Letter 具有给定因子和非重复字母的双无限幂自由词的构造
Pub Date : 2022-02-24 DOI: 10.1007/978-3-031-34326-1_12
Josef Rukavicka
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引用次数: 0
Sync-Maximal Permutation Groups Equal Primitive Permutation Groups 同步最大置换群等于原始置换群
Pub Date : 2021-11-26 DOI: 10.1007/978-3-030-93489-7_4
Stefan Hoffmann
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引用次数: 1
Commutative Regular Languages with Product-Form Minimal Automata 乘积形式最小自动机的可交换正则语言
Pub Date : 2021-11-26 DOI: 10.1007/978-3-030-93489-7_5
Stefan Hoffmann
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引用次数: 1
State Complexity Investigations on Commutative Languages - The Upward and Downward Closure, Commutative Aperiodic and Commutative Group Languages 可交换语言的状态复杂性研究——上下闭包、可交换非周期和可交换群语言
Pub Date : 2021-11-26 DOI: 10.1007/978-3-030-93489-7_6
Stefan Hoffmann
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引用次数: 1
Image-Binary Automata Image-Binary自动机
Pub Date : 2021-09-02 DOI: 10.1007/978-3-030-93489-7_15
S. Kiefer, C. Widdershoven
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引用次数: 0
Improved constructions for succinct affine automata 简练仿射自动机的改进构造
Pub Date : 2021-06-30 DOI: 10.1007/978-3-030-93489-7_16
A. Yakaryılmaz
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引用次数: 1
On the Uniform Distribution of Regular Expressions 正则表达式的均匀分布
Pub Date : 2021-03-24 DOI: 10.1007/978-3-030-93489-7_2
Sabine Broda, António Machiavelo, Nelma Moreira, Rogério Reis
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引用次数: 0
Regular Expression Length via Arithmetic Formula Complexity 正则表达式长度通过算术公式复杂度
Pub Date : 2020-12-31 DOI: 10.1007/978-3-030-62536-8_3
Ehud Cseresnyes, Hannes Seiwert
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引用次数: 2
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Workshop on Descriptional Complexity of Formal Systems
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