### On the task of extracting the root from the language

#### Abstract

In this paper,we consider a special case of constructing the inverse morphism for the given finite language: we try to extract the root from this language. For such extracting, we consider some special simple cases.

We shall firstly look at some special class of languages, for which the problem is solved easily. Namely, we describe this class, consider some examples, and give some obtained results of computer experiments. Then we define antiderivative roots and give some propositions that show, how to use antiderivative roots for obtaining any root of the given degree.

Then we give an interesting example, which refutes a possible simple algorithm for this task. Therefore, if there exists a polynomial-time algorithm that solves this problem, then it should be formulated more complicated.

We hope that the further development of the theory described in this paper will provide an opportunity to describe a polynomial-time algorithms for solving the general case of this problem.

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