Towards computer-assisted proofs of parametric Andrews-Curtis simplifications, II

6 pages•Published: May 26, 2024

Abstract

We present recent developments in the applications of automated theorem proving in the investigation of the Andrews-Curtis conjecture. We demonstrate previously unknown simplifications of groups presentations from a parametric family MSn(w∗) of trivial group presentations for n = 3, 4, 5, 6, 7, 8 (subset of well-known Miller-Schupp family). Based on the human analysis of these simplifications we formulate two conjectures on the structure of simplifications for the infinite family MSn(w∗), n ≥ 3.
This is an extended and updated version of the abstract [11] presented at AITP 2023 conference.

Keyphrases: andrews curtis conjecture, automated reasoning, combinatorial group theory

In: Nikolaj Bjørner, Marijn Heule and Andrei Voronkov (editors). LPAR 2024 Complementary Volume, vol 18, pages 131-136.

Links:	https://easychair.org/publications/paper/tkQS
	https://doi.org/10.29007/p2w1

BibTeX entry

@inproceedings{LPAR2024C:Towards_computer_assisted_proofs,
  author    = {Alexei Lisitsa},
  title     = {Towards computer-assisted proofs of parametric Andrews-Curtis simplifications, II},
  booktitle = {LPAR 2024 Complementary Volume},
  editor    = {Nikolaj Bjørner and Marijn Heule and Andrei Voronkov},
  series    = {Kalpa Publications in Computing},
  volume    = {18},
  publisher = {EasyChair},
  bibsource = {EasyChair, https://easychair.org},
  issn      = {2515-1762},
  url       = {/publications/paper/tkQS},
  doi       = {10.29007/p2w1},
  pages     = {131-136},
  year      = {2024}}

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