"Allan C. Wechsler" <acw@alum.mit.edu> wrote about:

[...] the name of the algorithm for determining whether a given permutation can be expressed as a product of given generators: it's the Furst-Hopcroft-Luks algorithm.

I should probably have responded earlier, when you mentioned you had learned the name from the Rubik's Cube list. I believe I introduced the algorithm there under that name. Since then, I have been reliably informed that the algorithm is more usually and properly known as Sims's algorithm. The paper by Furst, Hopcroft, and Luks was essentially a formalization and analysis of the algorithm that Charles C. Sims described in 1967. I regret the mistaken attribution. Dan