Stallings Foldings and Subgroups of Free Groups

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On hyperbolicity of free splitting and free factor complexes (2012, background): “In this case the construction of gx;y becomes much easier and boils down to using standard Stallings foldings (in the sense of [21], [31]) to get from x to y.”
Profinite semigroups and applications (2005, methodology): “There is a well-known algorithm to check this property, namely Stallings’ folding algorithm applied to the “flower automaton”, whose petals are labeled with the words ψ(A) [82, 46].”
Acylindrical hyperbolicity of groups acting on trees (2013, unknown): “However, let us give a direct proof of the lemma using Stallings core graphs (see [54] for an introduction to this method).”
Expansion of random graphs: new proofs, new results (2012, background): “For more information we refer the interested reader to [30,53] and especially to [42].”
Algebraic extensions in free groups (2006, background): “The notion of algebraic extension discussed in this paper was first introduced by Kapovich and Miasnikov [7].”