Synchronization problems in automata without non-trivial cycles

被引：9
|
作者：
Ryzhikov, Andrew [1 ,2 ,3 ]
机构：
[1] Univ Paris Est, LIGM, Marne La Vallee, France
[2] Univ Grenoble Alpes, Lab G SCOP, Grenoble, France
[3] NASB, United Inst Informat Problems, Minsk, BELARUS
来源：
THEORETICAL COMPUTER SCIENCE | 2019年 / 787卷
关键词：
Synchronizing automaton; Computational complexity; Inapproximability; Weakly acyclic automaton; Subset rank; Synchronizable set; SUBSET SYNCHRONIZATION; WORDS;
D O I：
10.1016/j.tcs.2018.12.026
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
We study the computational complexity of various problems related to synchronization of weakly acyclic automata, a subclass of widely studied aperiodic automata. We provide upper and lower bounds on the length of a shortest word synchronizing a weakly acyclic automaton or, more generally, a subset of its states, and show that the problem of approximating this length is hard. We investigate the complexity of finding a synchronizable set of states of maximum size. We also show inapproximability of the problem of computing the rank of a subset of states in a binary weakly acyclic automaton and prove that several problems related to recognizing a synchronizable subset of states in such automata are NP-complete. (C) 2019 Elsevier B.V. All rights reserved.
引用
收藏
页码：77 / 88
页数：12
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