A stable non-interleaving early operational semantics for the pi-calculus

We give the first non-interleaving early operational semantics for the pi-calculus which generalises the standard interleaving semantics and unfolds to the stable model of prime event structures. Our starting point is the non-interleaving semantics given for CCS by Mukund and Nielsen, where the so-called structural (prefixing or subject) causality and events are defined from a notion of locations derived from the syntactic structure of the process terms. We conservatively extend this semantics with a notion of extruder histories, from which we infer the so-called link (name or object) causality and events introduced by the dynamic communication topology of the pi-calculus. We prove that the semantics generalises both the standard interleaving early semantics for the pi-calculus and the non-interleaving semantics for CCS. In particular, it gives rise to a labelled asynchronous transition system unfolding to prime event structures

Diamonds for Security: A Non-Interleaving Operational Semantics for the Applied Pi-Calculus

We introduce a non-interleaving structural operational semantics for the applied ?-calculus and prove that it satisfies the properties expected of a labelled asynchronous transition system (LATS). LATS have well-studied relations with other standard non-interleaving models, such as Mazurkiewicz traces or event structures, and are a natural extension of labelled transition systems where the independence of transitions is made explicit. We build on a considerable body of literature on located semantics for process algebras and adopt a static view on locations to identify the parallel processes that perform a transition. By lifting, in this way, work on CCS and ?-calculus to the applied ?-calculus, we lay down a principled foundation for reusing verification techniques such as partial-order reduction and non-interleaving equivalences in the field of security. The key technical device we develop is the notion of located aliases to refer unambiguously to a specific output originating from a specific process. This light mechanism ensures stability, avoiding disjunctive causality problems that parallel extrusion incurs in similar non-interleaving semantics for the ?-calculus

Event structures for the reversible early internal pi-calculus

The pi-calculus is a widely used process calculus, which models com-munications between processes and allows the passing of communication links.Various operational semantics of the pi-calculus have been proposed, which canbe classified according to whether transitions are unlabelled (so-called reductions)or labelled. With labelled transitions, we can distinguish early and late semantics.The early version allows a process to receive names it already knows from the en-vironment, while the late semantics and reduction semantics do not. All existingreversible versions of the pi-calculus use reduction or late semantics, despite theearly semantics of the (forward-only) pi-calculus being more widely used than thelate. We define piIH, the first reversible early pi-calculus, and give it a denotationalsemantics in terms of reversible bundle event structures. The new calculus is a re-versible form of the internal pi-calculus, which is a subset of the pi-calculus whereevery link sent by an output is private, yielding greater symmetry between inputsand outputs

A network-conscious π-calculus and its coalgebraic semantics

Traditional process calculi usually abstract away from network details, modeling only communication over shared channels. They, however, seem inadequate to describe new network architectures, such as Software Defined Networks, where programs are allowed to manipulate the infrastructure. In this paper we present the Network Conscious @p-calculus ( NCPi), a proper extension of the @p-calculus with an explicit notion of network: network links and nodes are represented as names, in full analogy with ordinary @p-calculus names, and observations are routing paths through which data is transported. However, restricted links do not appear in the observations, which thus can possibly be as abstract as in the @p-calculus. Then we construct a presheaf-based coalgebraic semantics for NCPi along the lines of Turi-Plotkin's approach, by indexing processes with the network resources they use: we give a model for observational equivalence in this context, and we prove that it admits an equivalent nominal automaton (HD-automaton), suitable for verification. Finally, we give a concurrent semantics for NCPi where observations are multisets of routing paths. We show that bisimilarity for this semantics is a congruence, and this property holds also for the concurrent version of the @p-calculus

Event structure semantics for multiparty sessions

We propose an interpretation of multiparty sessions as "Flow Event Structures", which allows concurrency within sessions to be explicitly represented. We show that this interpretation is equivalent, when the multiparty sessions can be described by global types, to an interpretation of such global types as "Prime Event Structures"

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 π-calculus 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 peer- to-peer architecture Pastry. 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 binding: it introduces α-conversion and makes SOS rules and bisimulations non-standard. The consequence is that coalgebras on sets are not able to capture these notions. The idea of the seminal paper by Fiore and Turi is resorting to coalgebras on presheaves, i.e. functors C → Set. Intuitively, presheaves allow associating to collections of names, seen as objects of C, the set of processes using those names. Fresh names generation strategies can be formalized as endofunctors on C, which are lifted to presheaves in a standard way and used to model name binding. Within this framework, a coalgebra for the π-calculus transition system is constructed: the benefit is that ordinary coalgebraic bisimulations for such coalgebra are π-calculus bisimulations. Moreover, Fiore and Turi show a technique to obtain a new coalgebra whose bisimilarity is closed under all renamings. This relation is a congruence for the π-calculus. Presheaves come with a rich theory that can help deriving new results, but coalgebras on presheaves are impractical to implement: the state space can be infinite, for instance when a process recursively creates names. However, if we restrict to a class of presheaves (according to Ciancia et al.), coalgebras admit a concrete implementation in terms of HD-automata, that are finite-state automata suitable for verification. In this thesis we adapt and extend Fiore-Turi’s approach to cope with network resources. First we provide a coalgebraic semantics for NCPi whose bisimulations are bisimulations in the NCPi sense. Then we compute coalgebras and equivalences that are closed under all renamings. The greatest such equivalence is a congruence w.r.t. the input prefix and we conjecture that, for the NCPi with only guarded sums, it is a congruence also w.r.t. parallel composition. We show that this construction applies a form of saturation. Then we prove the existence of a HD-automaton for NCPi. The treatment of network resources is non-trivial and paves the way to modeling other calculi with complex resources