In this paper we consider 2-processor algorithms for simulating the be
haviour of given formulae over the basis {+}, where + denotes the two
argument Boolean function, Exclusive-Or. A sequence of 2-processor sim
ulation strategies [S-r] (r greater than or equal to 0) is described a
nd it is proved that the ratio ex(r)[n]/n approach 0.5, where ex(r)[n]
is the expected number of steps taken by S-r on n-node formulae gener
ated at random using the binary search tree distribution.