Unary finite automata vs. arithmetic progressions

被引：33
|
作者：
To, Anthony Widjaja [1 ]
机构：
[1] Sch Informat, Edinburgh EH8 9AB, Midlothian, Scotland
来源：
INFORMATION PROCESSING LETTERS | 2009年 / 109卷 / 17期
基金：
英国工程与自然科学研究理事会;
关键词：
Formal languages; Unary languages; Arithmetic progressions; Algorithms;
D O I：
10.1016/j.ipl.2009.06.005
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
We point out a subtle error in the proof of Chrobak's theorem that every unary NFA can be represented as a union of arithmetic progressions that is at most quadratically large. We propose a correction for this and show how Martinez's polynomial time algorithm, which realizes Chrobak's theorem. can be made correct accordingly. We also show that Martinez's algorithm cannot be improved to have logarithmic space, unless L = NL. (C) 2009 Elsevier B.V. All rights reserved.
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页码：1010 / 1014
页数：5
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