Categorical Structure of Asynchrony

Peter Selinger
1999 Electronical Notes in Theoretical Computer Science  
We investigate a categorical framework for the semantics of asynchronous communication in networks of parallel processes. Abstracting from a category of asynchronous labeled transition systems, we formulate the notion of a categorical model of asynchrony as a uniformly traced monoidal category with diagonals, such that every morphism is total and the focus is equivalent to a category of complete partial orders. We present a simple, non-deterministic, cpo-based model that satisfies these
more » ... ents, and we discuss how to refine this model by an observational congruence. We also present a general construction of passing from deterministic to non-deterministic models, and more generally, from non-linear to linear structure on a category. A category of asynchronous processes In this section, we describe a category of asynchronous labeled transition systems. This category, which was first introduced in [14], will serve us to motivate the more abstract categorical definitions of the later sections. Labeled transition systems and bisimulation Throughout, we will write RS for the composition of binary relations, i.e., xRSz if for some y, xRy and ySz. Definition 1.1 A labeled transition system is a tuple S = S, A, − →, s 0 , where S is a set of states, A is a set of actions, − →⊆ S×A×S is a transition relation, and s 0 ∈ S is the initial state. We also write |S| = S for the set of states. The set of actions A is also called the type of the labeled transition system S, and we write S : A. For the transition relation, we write s α − → t instead of s, α, t ∈ − →, and the intended interpretation is that the system can get from state s to state t by performing an action α.
doi:10.1016/s1571-0661(04)80073-2 fatcat:huz3xocq2vew5lm3kroexlvgoi