The use of heuristics such as Genetic Algorithm optimisation methods is appealing in a large range of inverse problems. The problem presented here deals with the mathematical analysis of sequences generated by finite automata. There is no known general exact method for solving the associated inverse problem. GA optimisation techniques can provide useful results, even in the very particular area of mathematical analysis. This paper presents the results we have obtained on the inverse problem for fixed point automata. Software implementation has been developed with the help of ALGON, our home-made Genetic Algorithm software.