一个量子比特可以零错误地分离任何一对单词吗？
Can one quantum bit separate any pair of words with zero-error?
摘要：
确定一个有限自动机分离一对给定的不同单词所需的最少状态数是一个重要的问题。在本文中，我们考虑这个问题的量子自动机（QFAs）。我们发现，2状态QFA可以分离任何一对的话在非确定性的接受模式和猜想，他们可以分离任何一对也与零错误。然后，我们专注于（一个更一般的问题）分离一对两个不相交的有限的词集。我们表明，QFA可以有效地分离它们在非确定性的接受模式，即状态的数量是2的小集合的大小的幂。此外，我们研究仿射有限自动机（AfAs），并表明，两个状态足以分离任何一对零错误。此外，AfAs可以有效地分离任何一对不相交的有限字集与单侧有界误差在非确定性模式下的QFA一样。
英文摘要：
Determining the minimum number of states required by a finite automaton to separate a given pair of different words is an important problem. In this paper, we consider this problem for quantum automata (QFAs). We show that 2-state QFAs can separate any pair of words in nondeterministic acceptance mode and conjecture that they can separate any pair also with zero-error. Then, we focus on (a more general problem) separating a pair of two disjoint finite set of words. We show that QFAs can separate them efficiently in nondeterministic acceptance mode, i.e. the number of states is two to the power of the size of the small set. Additionally, we examine affine finite automata (AfAs) and show that two states are enough to separate any pair with zero-error. Moreover, AfAs can separate any pair of disjoint finite sets of words with one-sided bounded error efficiently like QFAs in nondeterministic mode.
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。
