Automating Mathematics

Working journal

Andrews-Curtis: First Run

Finally having run something in ProvingGround involving the main learning method, here are some observations.

Simple Andrews-Curtis run

Starting with an initial distribution, evoution took place with the basic Andrews-Curtis moves. I ran two loops with two steps each, and then resumed and ran 3 more loops. The raw results are at first run results


  • In terms of the highest weights, the method worked well even with such a short run. For example, the presentation $\langle a, b; \bar{a}, b\rangle$ was one of those with high weight.

  • In general, the order was according to expected behaviour.

  • However, virtually all theorems were remembered.

  • This stems from two weaknesses:
    • two high a weight for theorems relative to proofs, leading to memos favoured over deduction.
    • not enough methods of deduction, specifically exlusion of multiplication-inversion moves.
  • These can be corrected by:
    • adding more moves: multiplication-inversions, transpositions; or allowing composite moves.
    • lowering the probability of word-continuation in generating presentations (just a runtime parameter).