here is some more info on the algorithm i briefly described yesterday.
the paper i have is "planning and learning in permutation groups", by
fiat, moses, shamir, shimshoni and tardos. it appeared in the 30th
annual symposium on foundations of computer science, pp 274-9.
the paper mentions that they have calculated all identities of length 16
(they count face turns). this means that the algorithm was successfully
implemented for the list L of all configurations within 4 face turns
also, alan gives a much more detailed description of this algorithm
in the archives. see his message of may 27, 1987 "shamir's talk really
was about how to solve the cube!" (cube-mail-6)
i encourage people to look up the paper and/or alan's message. this is
an exciting development, and the lack of attention this idea has
received is a shame.