Interaction and observation: categorical semantics of reactive systems trough dialgebras
Abstract
We use dialgebras, generalising both algebras and coalgebras, as a complement of the standard coalgebraic framework, aimed at describing the semantics of an interactive system by the means of reaction rules. In this model, interaction is built-in, and semantic equivalence arises from it, instead of being determined by a (possibly difficult) understanding of the side effects of a component in isolation. Behavioural equivalence in dialgebras is determined by how a given process interacts with the others, and the obtained observations. We develop a technique to inter-define categories of dialgebras of different functors, that in particular permits us to compare a standard coalgebraic semantics and its dialgebraic counterpart. We exemplify the framework using the CCS and the pi-calculus. Remarkably, the dialgebra giving semantics to the pi-calculus does not require the use of presheaf categories.
Keywords
Cite
@article{arxiv.1209.5903,
title = {Interaction and observation: categorical semantics of reactive systems trough dialgebras},
author = {Vincenzo Ciancia},
journal= {arXiv preprint arXiv:1209.5903},
year = {2013}
}