A Theory of Communicating Sequential Processes
Journal of the ACM (JACM)
Modeling concurrency with geometry
POPL '91 Proceedings of the 18th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Detecting Deadlocks in Concurrent Systems
CONCUR '98 Proceedings of the 9th International Conference on Concurrency Theory
Higher Dimensional Transition Systems
LICS '96 Proceedings of the 11th Annual IEEE Symposium on Logic in Computer Science
Homotopy invariants of higher dimensional categories and concurrency in computer science
Mathematical Structures in Computer Science
On the expressiveness of higher dimensional automata
Theoretical Computer Science - Expressiveness in concurrency
A category of higher-dimensional automata
FOSSACS'05 Proceedings of the 8th international conference on Foundations of Software Science and Computation Structures
Erratum: Erratum to “On the expressiveness of higher dimensional automata”
Theoretical Computer Science
Formal Relationships Between Geometrical and Classical Models for Concurrency
Electronic Notes in Theoretical Computer Science (ENTCS)
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The main idea for interpreting concurrent processes as labelled precubical sets is that a given set of n actions running concurrently must be assembled to a labelled n-cube, in exactly one way. The main ingredient is the non-functorial construction called the labelled directed coskeleton. It is defined as a subobject of the labelled coskeleton, the latter coinciding in the unlabelled case with the right adjoint to the truncation functor. This non-functorial construction is necessary since the labelled coskeleton functor of the category of labelled precubical sets does not fulfil the above requirement. We prove in this paper that it is possible to force the labelled coskeleton functor to be well behaved by working with labelled transverse symmetric precubical sets. Moreover, we prove that this solution is the only one. A transverse symmetric precubical set is a precubical set equipped with symmetry maps and with a new kind of degeneracy map called transverse degeneracy. Finally, we also prove that the two settings are equivalent from a directed algebraic topological viewpoint. To illustrate, a new semantics of the calculus of communicating systems (CCS), equivalent to the old one, is given.