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Applying Gödel's Dialectica Interpretation to Obtain a Constructive Proof of Higman's Lemma (1210.3117v1)
Published 11 Oct 2012 in cs.LO and cs.DM
Abstract: We use G\"odel's Dialectica interpretation to analyse Nash-Williams' elegant but non-constructive "minimal bad sequence" proof of Higman's Lemma. The result is a concise constructive proof of the lemma (for arbitrary decidable well-quasi-orders) in which Nash-Williams' combinatorial idea is clearly present, along with an explicit program for finding an embedded pair in sequences of words.