The Closest Substring problem asks whether there exists a consensus string w of given length ℓ such that each string in a set of strings L has a substring whose edit distance is at most r (called the radius) from w. The Closest Substring problem has been studied for finite sets of strings and is known to be NP-hard. We show that the Closest Substring problem for regular languages represented by nondeterministic finite automata (NFA) is PSPACE-complete. The problem remains PSPACE-hard even when the input is a deterministic finite automaton and the length ℓ and radius r are given in unary. Also we show that the Closest Substring problem for acyclic NFAs lies in the second level of the polynomial-time hierarchy and is both NP-hard and coNP-hard.

在最近的子串问题询问是否存在一个共识串瓦特给定长度的ℓ使得在一组串的每个字符串大号具有其子串编辑距离是至多ř从（称为半径）瓦特。在最近的子串问题已经研究了有限集串和已知是NP -hard。我们表明，由不确定性有限自动机（NFA）表示的常规语言的最接近子字符串问题是PSPACE -complete。即使输入是确定性有限自动机和长度，问题仍然是PSPACE难以解决的ℓ和半径r以一元形式给出。我们还表明，非循环NFA的最近子串问题位于多项式时间层次结构的第二级，并且是NP - hard和coNP-hard。