The consensus string (or centre string, closest string) of a set S of strings is defined as a string which is within a radius r from all strings in S. We study the consensus string problem for multiple languages recognized by finite automata (FAs). We define the consensus string of languages to be within distance at most r to some string in each of the languages. We also study the decidability and computational complexity of the consensus string problem for multiple formal language instances. We show that the consensus string problem for multiple regular languages is $\mathsf{PSPACE}$-complete even when the radius r is fixed. We prove that the problem can be solved in polynomial time when the number of languages is fixed. Finally, we study that the consensus string problem for the class of input-driven languages and show that the problem is decidable.

字符串集合S的共识字符串（或中心字符串、最接近字符串）被定义为一个字符串，该字符串在S 中所有字符串的半径r内。我们研究了有限自动机 (FA) 识别的多种语言的共识字符串问题。我们将语言的共识字符串定义为与每种语言中的某个字符串的距离最多为r。我们还研究了多个形式语言实例的共识字符串问题的可判定性和计算复杂性。我们证明了多种正则语言的共识字符串问题是$\mathsf{空间}$- 即使半径r是固定的，也能完成。我们证明了当语言数量固定时，该问题可以在多项式时间内解决。最后，我们研究了输入驱动语言类的共识字符串问题，并表明该问题是可判定的。