  We describe an algorithm to subdivide automatically a given set of PL
n-manifolds (via coloured triangulations or, equivalently, via
crystallizations) into classes whose elements are PL-homeomorphic. The
algorithm, implemented in the case n=4, succeeds to solve completely the
PL-homeomorphism problem among the catalogue of all closed connected PL
4-manifolds up to gem-complexity 8 (i.e., which admit a coloured triangulation
with at most 18 4-simplices). Possible interactions with the (not completely
known) relationship among different classification in TOP and DIFF=PL
categories are also investigated. As a first consequence of the above PL
classification, the non-existence of exotic PL 4-manifolds up to gem-complexity
8 is proved. Further applications of the tool are described, related to
possible PL-recognition of different triangulations of the K3-surface.
