Plans regarding the running report (including the MRes dissertation) of MG.
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Plans regarding the running report (including the MRes dissertation) of MG.
 Todo:
 Fix binary cardinality constraints lemmas

The binary cardinality constraints lemmas use the notion of arcconsistency, but should use the notion of strongly r_kbased developed during discussions and in the OKlibrary.
 Todo:
 Add lemmas and definitions for *all* "nonclashing" matrices results

There are better equations for counting the number of nonclashing matrices, defined in the OKlibrary. Their definitions and proofs of correctness etc, should be added to this document.
 Todo:
 Tidy "nonclashing matrices" lemmas

Some of the lemmas are using notations such as etc, which are inappropriate and should be replaced with more reasonable notations.

There also needs to be more flow between lemmas.
 Todo:
 Define target(s) for PhD

There should be an overall target (basic aim for thesis etc) with a variety of *welldefined* subtargets which are reachable and can be used as objectives in any timelines.
 Todo:
 Update "Clauseset representations" section

This section was created initially to move the deterministic input, deterministic output lemma into (given it's inappropriateness for the data analysis document at this time).

This section should be fleshed out with questions, conjectures, definitions etc, which can then later be moved to the data analysis document.
 Todo:
 Update "AES" section with latest definitions

The running document and MRes thesis are out of sync and the MRes thesis has newer proofs regarding various key details.

The proofs, notations etc also should be improved.

Various historical explanation etc should be moved elsewhere or removed completely.
 Todo:
 Update "Representations of boolean functions" section with latest proofs.

The running document and MRes thesis are out of sync and the MRes thesis has newer proofs regarding various key details.

The proofs, notations etc also should be improved.
 Todo:
 Finish topological proof of vdW theorem section

This is necessary due to the need for a submitted report for the MRes.

When transferring the document to the running report, then (thorough!) editorial corrections are needed.

And complete references are needed.

See "Writeup van der Waerden's theorem and proofs" below: These todos seem to need updating.
 Todo:
 Cardinality constraints

W.r.t. the topic of "good" representations of conditions, cardinality constraint yield examples (not much of interest without using new variables, but some (accessible) literature exploring the use of new variables).

Especially interesting claims of "optimal" representations.
 Todo:
 Consider preprocessing / recombination idea w.r.t. PHP

Consider initial example of covering and then CNF>DNF>CNF translation within the context of the PHP formula.

One example of a particular covering might be considering a single pigeon every hole, then this for each pigeon.

Such preprocessing might make the problem easier and if automated would be very useful/interesting.
 Todo:
 Clause set automorphisms vs Ramsey problem automorphisms

Add/expand considerations of whether the symmetries on the problem space are all the symmetries of the SAT problem.
 Todo:
 Literature research

Of utmost importance is a thorough literature research.

All basic literature, and all papers regarding bounds for Ramsey numbers must be gathered.
 Todo:
 Ten challenges
 Todo:
 More precision

All usage of "magical symbols" must be eliminated.

And all extremes cases need to be discussed (and compared w.r.t. implementations in the OKlibrary).
 Todo:
 Add section on combinatorial enumeration
 Todo:
 Writeup Ramsey's theorem and proofs

Obtain an overview on the existing proofs.

Extracting the upper and lower bounds for the OKlibrary.
 Todo:
 Update and extend generators for Ramsey problems

Create links to relevant other parts of the library.

Organise the various efforts.

Writeup proof for symmetry breaking using Ramsey numbers for smaller parameters.
 Todo:
 Evaluation of measures

Create links to relevant other parts of the library.

Make plans how to proceed.
 Todo:
 Symmetries of Ramsey problems

Create links to relevant other parts of the library.

Make an extensive literature search.

Organise the various efforts.
 Todo:
 Various Ramsey type problems to be investigated

Obtain an overview on "Ramsey type" problems.

Make an extensive literature search.

Make some plans which other Ramsey type problems to investigate.
 Todo:
 Tuning and understanding of local search

Create links to relevant other parts of the library.

Make an extensive literature search on ways of "understanding" local search procedures.

One topic is the analysis of the optimisation space.
 Todo:
 Solvers and tools for solving Ramsey problems

Create links to relevant other parts of the library.

Install all reasonable tools, and create Rscripts to run them.
 Todo:
 Exploiting solution patterns

There are some SAT articles for van der Waerden problems, which must be explored.

Develop some research program for finding and exploiting patterns.

The general topic is the structure of the solution space.

The basic structure is that of a set of partial assignments.

So we have a boolean function.

Also visualisations can be explored.
 Todo:
 Make solutions from the literature available

That R_N(5,5; 2) >= 43 is based on concrete solutions  represent them.
 Todo:
 Special methods

Investigate in detail [McKay, Radziszowski, 1997, Journal of Combinatorial Theory, Series B].
 Todo:
 Processing of [Introduction to Boolean Algebras]

The task is to completely process the book:

All definitions extracted and made precise (of course, adapting the notations and notions if needed).

All results extracted as lemmas and theorems, with full proofs.

All exercises solved, and integrated into the text (as lemmas and examples).

Roughly one section every two weeks, so that in about 1 1/2 years the book has been completely processed.
 Todo:
 Update "Data matrices" section : DONE

Write up definitions and lemma regarding the recursive definition for the number of noncontradictory matrices. DONE

Write up proof of conjecture (from existing proof on paper). DONE

Further work on the notations is needed to tie in nicely with the Data analysis document, and to introduce definitions only when the notions will be used elsewhere (DONE  Moved to Tidy "nonclashing matrices" lemmas).
Definition in file RunningReportMG.hpp.