Tuesday, June 28, 2011

two more conjectures

The first one is wholly my own, and this one I have a lot less data to base it on than others, and I can't even really say why I think it might be true. However, it's something for me to spend some time (using the nifty new "search for a strategy (interactively)" functionality, which I am loving) investigating, and it doesn't seem prima facie false:
Conjecture: Let s be a winning E-strategy for phi. Extend s to s' by augmenting the tree wherever required so that the result is a winning D-strategy. Claim: The E-violating moves will occur after P has asserted an atom.

Check back often for evidence for or against this conjecture.

The second one is one that Chris proposed, namely whether D10+D12+D13=CL (i.e., we drop E, but add D12). Now, you might recall from a week or two ago that I conjectured that D10+D12+D13=IL, not CL (and I already have an easy proof that D10+D11+D13=IL), so it will be interesting to see how this pans out.

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