In this paper, we propose a new linear-time complexity algorithm that generates the regular expression of a labelled transition system (LTS), i.e., its language. The LTS represents the behaviour of a system such that each path witnesses a possible execution, and such that the language consists of all the possible executions. This contribution is then used to ensure the well-known label coverage criterion in model-based testing. Given an LTS under test, the objective is to find as few and as short paths as possible that cover all the labels/actions of the system to generate significant test inputs. To reach this goal, our second contribution in this paper is to formulate this problem as an Integer Linear Program (ILP) involving the set of finite paths of the system that will be extracted from the regular expression of the LTS. Our approach is validated through a prototype and evaluated on some toy examples, as well as randomly generated LTS, to highlight its feasibility and limits.