## Paper: A Sheaf-Theoretic Model of Concurrency (at LICS 1986)

**Luís F. Monteiro Fernando C. N. Pereira**

### Abstract

We develop here a structural theory of concurrency in which
the locality of interaction between subsystems is described with the
mathematical tools of the theory of sheaves. This theory allows us to model
precisely processes that interact through common behavior at shared
locations. In contrast to behavioral models, ours keeps track of the individual
contributions of subsystems to overall system behavior, allowing a
finer-grained analysis of subsystem interactions.

From event signatures that specify relations of independence and exclusivity
between events, we construct spaces of locations where activity may
occur. Behaviors are then modeled as elements of sheaves of monoids over those
spaces and processes as certain sets of behaviors. The construction of the
model, and in particular ist avoidance of interleaving, gives it very
convenient mathematical properties - sheaves of behavior monoids are to event
signatures what free monoids are to alphabets. The theory also allows us to
identify on purely structural grounds event signatures with a potential for
deadlock.

We conclude with a discussion of the solution of process equations in our model,
with an example from CSP.

### BibTeX

@InProceedings{MonteiroPereira-ASheafTheoreticMode, author = {Luís F. Monteiro and Fernando C. N. Pereira}, title = {A Sheaf-Theoretic Model of Concurrency}, booktitle = {Proceedings of the First Annual IEEE Symposium on Logic in Computer Science (LICS 1986)}, year = {1986}, month = {June}, pages = {66--76}, location = {Cambridge, MA, USA}, publisher = {IEEE Computer Society Press} }