  We give a formalization of Pratt's intuitive sculpting process for
higher-dimensional automata (HDA). Intuitively, an HDA is a sculpture if it can
be embedded in (i.e., sculpted from) a single higher dimensional cell
(hypercube). A first important result of this paper is that not all HDA can be
sculpted, exemplified through several natural acyclic HDA, one being the famous
"broken box" example of van Glabbeek. Moreover, we show that even the natural
operation of unfolding is completely unrelated to sculpting, e.g., there are
sculptures whose unfoldings cannot be sculpted. We investigate the
expressiveness of sculptures, as a proper subclass of HDA, by showing them to
be equivalent to regular ST-structures (an event-based counterpart of HDA) and
to (regular) Chu spaces over 3 (in their concurrent interpretation given by
Pratt). We believe that our results shed new light on the intuitions behind
sculpting as a method of modeling concurrent behavior, showing the precise
reaches of its expressiveness. Besides expressiveness, we also develop an
algorithm to decide whether an HDA can be sculpted. More importantly, we show
that sculptures are equivalent to Euclidean cubical complexes (being the
geometrical counterpart of our combinatorial definition), which include the
popular PV models used for deadlock detection. This exposes a close connection
between geometric and combinatorial models for concurrency which may be of use
for both areas.
