FreeWillConfiguration.hpp File Reference

Plans regarding the point-configuration in the [Conway; Free Will]-paper. More...

Go to the source code of this file.

Detailed Description

Plans regarding the point-configuration in the [Conway; Free Will]-paper.

Detailed examination of Peres33PointConfiguration.cnf
  • W.r.t. the number of variables or number of clauses the smallest minimally unsatisfiable sub-clause-set.
  • Also counting all minimally unsatisfiable and maximally satisfiable sub-clause-sets.
  • And the largest satisfiable sub-clause-set (32 clauses)
  • Should be lean.
  • Necessary and potentially necessary clauses etc. ({-1,-2,-3} is necessary, and also the associated 2-clauses; removing the whole triple 1,8,9 also renders it sat, and this seems to hold for all triples; it seems that also all binary clauses coming from the "free pairs" are necessary --- so perhaps all 33 variables are needed).
  • Based on the symmetries of the underlying figure, it should be not too hard to determine the symmetries of the cnf.
  • Resolution complexity
  • Is there some special structure? ,/ul>

    Testing realisability
    • Test the conjecture that every graph with a circuit of length 4 is orthogonally realisable.
    • A stronger conjecture is that after fulfilling all forced choices (given by triplets) via an arbitrary traversal (in the sense as developed in CS-232) and making always random choices exactly the realisable graphs are realised with high probability. For this we need to create random graphs without cycles of length 4.
    • Of course, a first test is performed with the hypergraph from the Peres configuration.
    Minimal configuration
    • What is the minimal number of vertices in a realisable graph which is not 101-colourable? Develop plans to attack this problem.

Definition in file FreeWillConfiguration.hpp.