We provide alternative proofs and algorithms for resultsproved by Sénizergues on rational and recognizable freegroup languages. We consider two different approaches to the basicproblem of deciding recognizability for rational free group languagesfollowing two fully independent paths: the symmetrificationmethod (using techniques inspired by the study ofinverse automata and inverse monoids) andthe right stabilizer method (a general approach generalizable to otherclasses of groups). Several different algorithmic characterizations ofrecognizability are obtained, as well as other decidability results.
