This document consists of a slightly revised and corrected version of a dissertation

Network programming is notoriously hard to understand: one has to deal with a variety of protocols (IP, ICMP, UDP, TCP etc), concurrency, packet loss, host failure, timeouts, the complex sockets interface to the protocols, and subtle portability issues. Moreover, the behavioural properties of operating systems and the network are not well documented.

Abstract. We propose a typing system for the true concurrent model of event structures that guarantees an interesting behavioural property known as confusion freeness. A system is confusion free if nondeterministic choices are localised and do not depend on the scheduling of independent components. It is a generalisation of confluence to systems that allow nondeterminism. Ours is the first typing system to control behaviour in a true concurrent model. To demonstrate its applicability, we show that typed event structures give a semantics of linearly typed version of the π-calculi with internal mobility. The semantics we provide is the first event structure semantics of the π-calculus and generalises Winskel’s original event structure semantics of CCS. 1

Abstract. Nominal calculi have been shown very effective to formally model a variety of computational phenomena. The models of nominal calculi have often infinite states, thus making model checking a difficult task. In this note we survey some of the approaches for model checking nominal calculi. Then, we focus on History-Dependent automata, a syntax-free automaton-based model of mobility. History-Dependent automata have provided the formal basis to design and implement some existing verification toolkits. We then introduce a novel syntax-free setting to model the symbolic semantics of a nominal calculus. Our approach relies on the notions of reactive systems and observed borrowed contexts introduced by Leifer and Milner, and further developed by Sassone, Lack and Sobocinski. We argue that the symbolic semantics model based on borrowed contexts can be conveniently applied to web service discovery and binding. 1

Abstract. We propose the first compositional event structure semantics for a fully expressive π-calculus, generalising Winskel’s event structures for CCS. The π-calculus we model is the πI-calculus with recursive definitions and summations. First we model the synchronous calculus, introducing a notion of dynamic renaming to the standard operators on event structures. Then we model the asynchronous calculus, for which a new additional operator, called rooting, is necessary for representing causality due to new name binding. The semantics are shown to be operationally adequate and sound with respect to bisimulation. 1

Summary. Mobility is a central feature of many distributed systems of ever growing complexity. To make their formal analysis and verification feasible, process algebras — notably the π-calculus — have been introduced and extensively studied. A well-established method of verifying the correctness of general distributed systems has been model-checking which is completely automatic and relatively fast compared to other alternatives, and so particularly attractive in industrial context. Mobile systems are highly concurrent causing state space explosion when applying model-checking techniques. To cope with this problem, techniques based on partial order semantics of concurrency seem to offer the desired level of efficiency. The aim of this paper is to investigate how one of such techniques — based of unfoldings of high-level Petri nets — could be used for verification of π-calculus terms. Our starting point was an existing compositional translation from a finite fragment of the π-calculus into a class of high-level Petri nets. We developed a prototype tool based on this theoretical translation and an existing efficient unfolder and verifier. In this paper, we describe initial experimental results in support of specific design choices. Crucially, developing the prototype was not a straightforward task since the theoretical translation does not produce nets which conform to the input format required by the verifier. The paper states how this mismatch has been overcome and draws conclusions for future uses of unfoldings technique in the modelchecking of mobile systems.

Abstract. We propose a coalgebraic model of the Fusion calculus based on HD-automata. The main advantage of the approach is that the partition refinement algorithm designed for HD-automata is easily adapted to handle Fusion calculus processes. Hence, the transition systems of Fusion calculus processes can be minimised according to the notion of observational semantics of the calculus. As a beneficial side effect, this also provides a bisimulation checker for Fusion calculus. 1

Abstract. We propose the first compositional event structure semantics for a very expressive π-calculus, generalising Winskel’s event structures for CCS. The π-calculus we model is the πI-calculus with recursive definitions and summations. First we model the synchronous calculus, introducing a notion of dynamic renaming to the standard operators on event structures. Then we model the asynchronous calculus, for which a new additional operator, called rooting, is necessary for representing causality due to new name binding. The semantics are shown to be operationally adequate and sound with respect to bisimulation. 1

We study three operational models of name-passing process calculi: coalgebras on (pre)sheaves, indexed labelled transition systems, and history dependent automata. The coalgebraic model is considered both for presheaves over the category of finite sets and injections, and for its subcategory of atomic sheaves known as the Schanuel topos. Each coalgebra induces an indexed labelled transition system. Such transition systems are characterised, relating the coalgebraic approach to an existing model of name-passing. Further, we consider internal labelled transition systems within the sheaf topos, and axiomatise a class that is in precise correspondence with the coalgebraic and the indexed labelled transition system models. By establishing and exploiting the equivalence of the Schanuel topos with a category of named-sets, these internal labelled transition systems are also related to the theory of history dependent automata. Operational models of concurrent computation typically describe processes in terms of a state space together with its possible evolution by performing atomic actions. Transition systems have proved useful in modelling the kinds of processes involved in static networks, like those described by CCS and related calculi. In these situations, processes evolve by communicating along named channels. Modern systems, though, often contain an element of mobility and reconfiguration. In languages such as the π-calculus, this dynamic structure is described in terms of the communication of the channel names themselves: name-passing. This allows, for instance, one process to advise another process to begin communicating on a particular channel. Not surprisingly, techniques and models relevant to static networks are inadequate in the name-passing context. Thus operational models of name-passing process calculi have been investigated. ⋆ This paper supersedes the extended abstract with the same title that appeared in

Abstract. The finite π-calculus has an explicit set-theoretic functor-category model that is known to be fully abstract for strong late bisimulation congruence. We characterize this as the initial free algebra for an appropriate set of operations and equations in the enriched Lawvere theories of Plotkin and Power. Thus we obtain a novel algebraic description for models of the π-calculus, and validate an existing construction as the universal such model. The algebraic operations are intuitive, covering name creation, communication of names over channels, and nondeterminism; the equations then combine these features in a modular fashion. We work in an enriched setting, over a “possible worlds ” category of sets indexed by available names. This expands significantly on the classical notion of algebraic theories, and in particular allows us to use nonstandard arities that vary as processes evolve. Based on our algebraic theory we describe a category of models for the π-calculus, and show that they all preserve bisimulation congruence. We develop a direct construction of free models in this category; and generalise previous results to prove that all free-algebra models are fully abstract. 1