一元有限自动机与算术级数
Unary finite automata vs. arithmetic progressions
摘要：
我们指出一个微妙的错误，在证明Chrobak的定理，每一个一元NFA可以表示为一个联盟的算术级数是最大的平方。我们提出了一个更正，并显示如何马丁内斯的多项式时间算法，实现Chrobak定理，可以相应地正确。我们还表明，Martinez的算法不能被改进为具有对数空间，除非L = NL。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
