OKlibrary  0.2.1.6
RunningReportML.hpp File Reference

Plans regarding the running report of ML. More...

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Detailed Description

Plans regarding the running report of ML.

For the PhD-dissertation see Annotations/plans/MLDissertation.hpp

Todo:
Using homomorphisms in resolution proofs
  • Obtain an overview on the literature of symmetries in resolution proofs (starting with Krisnamurthy, then Urquhart, then Arai/Urquhart).
  • Obtain on overview on Szeider's extensions by homomorphisms.
  • If possible, obtain the journal- or conference-versions (more authoritative than preprints).
  • Always have complete references (using Latex_bib/TempML.bib, if needed).
  • Summarise these definitions/results, structuring the discussions by using lemmas, theorems and definitions.
  • Also relate to our notions and constructions (e.g., different categories).
Todo:
Relating isomorphisms of clause-sets with isomorphisms of graphs
  • Consider [The complexity of homomorphisms ..., Buening, Xu] from our point of view, using categories and functors.
  • Find better proofs!
  • The reductions of the graph isomorphism problems to isomorphisms of (various types of clause-sets) should be possible via the functors from graphs to clause-sets.
  • And for the other direction (finding clause-set-isomorphisms via graph-isomorphisms) see module Symmetries in the OKlibrary.
  • One should look at the specific constructions from the paper above (whether they yield something new).
  • For all the constructions (also for example those in the logic-programming-paper) we need to find out whether these are functors (or can be made functors).
Todo:
Relations to graph theory
  • For graph theory we need some nice overviews.
  • See [Hell, In introduction to the category of graphs].
Todo:
Bicliques
  • For finding "good" bicliques, get some overview on the literature.
Todo:
Biclique partitions
  • Literature overview on complexity/algorithms regarding biclique partitions.

Definition in file RunningReportML.hpp.