From:

~~~ Subject:

1. The length of Start is of course 0 qturns.

2. The length of Pons Asinorum is of course 12 qturns. This result

has been known since 1980. However, in the process of testing

out half-depth searches, I tested Pons Asinorum and encountered

a minor surprise. There are five "halfway" positions which

are unique up to M-conjugacy. I only expected three. They

are:

a. (RRLL)(FF) expected -- continue BB etc. b. (RRLL)(FB) expected -- continue FB etc. c. (RRLL)(FB') expected -- continue FB' etc. d. (FB')(RRLL) a surprise to me e. (RL')(FB')(RL') a surprise to me

3. The length of Pons Asinorum composed with Superflip is

20 qturns. Half-depth searches through level 9 found nothing.

A half-depth search at level 10 found ten "halfway" positions which

are unique up to M-conjugacy. I have my usual trouble of spinning

tapes containing representative elements in order to find the

processes, but I should have them in a couple of days or so.

I expect we will find that many (or all) of them are really

closely related, differing only by commuting in fairly trivial

ways, just as do the five half-way positions for Pons Asinorum.

4. The length of Superflip is 24 qturns. Half-depth searches

through level 11 found nothing, so the length is greater than

22. Mike Reid has found a Superflip process of length 24.

Hence, the length is 24. It would be more satisfying if I

could perform a half-depth search to level 12, but the

problem is just too big. Hence, I have no idea how

many "halfway" positions there are which are unique up to

M-conjugacy.

= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = Robert G. Bryan (Jerry Bryan) (304) 293-5192 Associate Director, WVNET (304) 293-5540 fax 837 Chestnut Ridge Road BRYAN@WVNVM Morgantown, WV 26505 BRYAN@WVNVM.WVNET.EDU