Denis B wrote:
Once more, you're just trying to create a diversion so that you don't have to admit your approach didn't lead you to the well defined nrczt concept
I have never said that my approach led me, or anyone, to the well-defined but narrower nrczt concept. Thus, there is nothing to admit.
The fact that a technique was not well publicized, nor well-used, is not relevant. I merely indicated that TM's existed, when they existed, and their logical equivalence, in restricted cases, to nrczt chains.
Regarding the counting technique: I have always indicated that I am not a big fan of using the technique. I mentioned it, from time to time, in hopes that someone will find a better way to humanly utilyze a similar approach. Matrix counting is not specific to TM's. However, it can be used. One can tailor the counting to specific matrix forms, and proceed with as restricted or as general a search as one wishes based upon both the matrix type(s) and tolerance of grouping.
The hpl in the Easter monster was uncovered using such a restricted form of counting, (a simple two dimensional per node count). This is not bragging, as the hpl is a symmetric PM which is therefor of minimal complexity. I was stunned to stumble upon such an easy elimination pattern in a famous and presumably oft analyzed puzzle.
The point here is that recognition of the matrix structure sometimes can uncover with
relative ease that which both computer programs and other techniques may fail to uncover.
Finally, and I mean finally: we may best agree to have a vast difference of opinion regarding these issues. In the future, I shall modify my comments when I find a TM elimination that happens to parrellel a t chain as follows, unless you take exception:
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Here is an elimination. Here is the justification I found. This justification mirrors a t chain, but with the following exceptions (if any)
In the specific case which started this unfortunate discussion, I would mention something like: the chain is not strictly any type of t chain defined by Denis B. because it uses a "cell" derived from a uniqueness argument. Furthermore, it ignores the strict ordering of "cell" consideration.
Have a fine day!