English

Applying G\"odel's Dialectica Interpretation to Obtain a Constructive Proof of Higman's Lemma

Logic in Computer Science 2012-10-12 v1 Discrete Mathematics

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.

Keywords

Cite

@article{arxiv.1210.3117,
  title  = {Applying G\"odel's Dialectica Interpretation to Obtain a Constructive Proof of Higman's Lemma},
  author = {Thomas Powell},
  journal= {arXiv preprint arXiv:1210.3117},
  year   = {2012}
}

Comments

In Proceedings CL&C 2012, arXiv:1210.2890