  We study the problem of computing the reachable principals of simulation
preorder and the reachable blocks of simulation equivalence. Following a
theoretical investigation of the decidability and complexity aspects of this
problem, which in particular highlights a stark contrast with the already
settled case of bisimulation, we design algorithms to solve this problem by
leveraging the idea of interleaving reachability and simulation computation
while possibly avoiding the computation of all the reachable states or the
whole simulation preorder. In particular, we put forward a symbolic algorithm
processing state partitions and, in turn, relations between their blocks, which
is suited for processing infinite state systems.
