A Network-Aware Process Calculus for Global Computing and its Categorical Framework

An essential aspect of distributed systems is resource management, concerning how resources can be accessed and allocated. This aspect should also be taken into account when modeling and verifying such systems. A class of formalisms with the desired features are nominal calculi: they represent resources as atomic objects called names and have linguistic constructs to express creation of new resources. The paradigmatic nominal calculus is the π-calculus, which is well-studied and comes with models and logics. The first objective of this thesis is devising a natural and seamless extension of the πcalculus where resources are network nodes and links. The motivation is provided by a recent, successful networking paradigm called Software Defined Networks, which allows the network structure to be manipulated at runtime via software. We devise a new calculus called Network Conscious π-calculus (NCPi), where resources, namely nodes and links, are represented as names, following the π-calculus guidelines. This allows NCPi to reuse the π-calculus name-handling machinery. The semantics allows observing end-to-end routing behavior, in the form of routing paths through the network. As in the π-calculus, bisimilarity is not closed under input prefix. Interestingly, closure under parallel composition does not hold either. Taking the greatest bisimulation closed under all renamings solves the issue only for the input prefix. We conjecture that such closure yields a full congruence for the subcalculus with only guarded sums. We introduce an extension of NCPi (κNCPi) with some features that makes it closer to real-life routing. Most importantly, we add concurrency, i.e. multiple paths can be observed at the same time. Unlike the sequential version, bisimilarity is a congruence from the very beginning, due to the richer observations, so κNCPi can be considered the “right” version of NCPi when compositionality is needed. This extended calculus is used to model the peerto-peer architecture Pastry [59]. The second objective is constructing a convenient operational model for NCPi. We consider coalgebras, that are categorical representation of system. Coalgebras have been studied in full generality, regardless of the specific structure of systems, and algorithms and logics have been developed for them. This allows for the application of general results and techniques to a variety of systems. The main difficulty in the coalgebraic treatment of nominal calculi is the presence of name