4 research outputs found
The Glory of the Past and Geometrical Concurrency
This paper contributes to the general understanding of the geometrical model
of concurrency that was named higher dimensional automata (HDAs) by Pratt. In
particular we investigate modal logics for such models and their expressive
power in terms of the bisimulation that can be captured. The geometric model of
concurrency is interesting from two main reasons: its generality and
expressiveness, and the natural way in which autoconcurrency and action
refinement are captured. Logics for this model, though, are not well
investigated, where a simple, yet adequate, modal logic over HDAs was only
recently introduced. As this modal logic, with two existential modalities,
during and after, captures only split bisimulation, which is rather low in the
spectrum of van Glabbeek and Vaandrager, the immediate question was what small
extension of this logic could capture the more fine-grained hereditary history
preserving bisimulation (hh)? In response, the work in this paper provides
several insights. One is the fact that the geometrical aspect of HDAs makes it
possible to use for capturing the hh-bisimulation, a standard modal logic that
does not employ event variables, opposed to the two logics (over less
expressive models) that we compare with. The logic that we investigate here
uses standard past modalities and extends the previously introduced logic
(called HDML) that had only forward, action-labelled, modalities. Besides, we
try to understand better the above issues by introducing a related model that
we call ST-configuration structures, which extend the configuration structures
of van Glabbeek and Plotkin. We relate this model to HDAs, and redefine and
prove the earlier results in the light of this new model. These offer a
different view on why the past modalities and geometrical concurrency capture
the hereditary history preserving bisimulation. Additional correlating insights
are also gained.Comment: 17 pages, 7 figure
Sculptures in Concurrency
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