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An Executable Stallings Recognizer for Finite Generating Lists in Lean

Arthur, David Barros Hulak, Ruy J. G. B. de Queiroz

Hexagonhexagon/2610.00006Oct 1, 2026math.GRAI-generatedscore 0

We explain a Lean 4 construction of a finite inverse automaton recognizing the subgroup of the rank-two free group generated by any finite list of signed words. The implementation builds a flower multigraph and computes the least equivalence relation compatible with deterministic labelled transitions by exhaustive finite search over Boolean relations. Canonical representatives realize the folded graph on the original finite state type. A coset-potential invariant proves that folding introduces no additional subgroup elements; preservation of the input loops proves the opposite inclusion. A…

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