Trees from Functions as Processes

Levy-Longo Trees and Bohm Trees are the best known tree structures on the {\lambda}-calculus. We give general conditions under which an encoding of the {\lambda}-calculus into the {\pi}-calculus is sound and complete with respect to such trees. We apply these conditions to various encodings of the call-by-name {\lambda}-calculus, showing how the two kinds of tree can be obtained by varying the behavioural equivalence adopted in the {\pi}-calculus and/or the encoding

Session types revisited

Session types are a formalism used to model structured communication-based programming. A binary session type describes communication by specifying the type and direction of data exchanged between two parties. When session types and session processes are added to the syntax of standard π-calculus they give rise to additional separate syntactic categories. As a consequence, when new type features are added, there is duplication of effort in the theory: the proofs of properties must be checked both on standard types and on session types. We show that session types are encodable into standard π- types, relying on linear and variant types. Besides being an expressivity result, the encoding (i) removes the above redundancies in the syntax, and (ii) the properties of session types are derived as straightforward corollaries, exploiting the corresponding properties of standard π-types. The robustness of the encoding is tested on a few extensions of session types, including subtyping, polymorphism and higher-order communications

Separability in the Ambient Logic

The \it{Ambient Logic} (AL) has been proposed for expressing properties of process mobility in the calculus of Mobile Ambients (MA), and as a basis for query languages on semistructured data. We study some basic questions concerning the discriminating power of AL, focusing on the equivalence on processes induced by the logic $(=_L>)$. As underlying calculi besides MA we consider a subcalculus in which an image-finiteness condition holds and that we prove to be Turing complete. Synchronous variants of these calculi are studied as well. In these calculi, we provide two operational characterisations of $_=L$: a coinductive one (as a form of bisimilarity) and an inductive one (based on structual properties of processes). After showing $_=L$ to be stricly finer than barbed congruence, we establish axiomatisations of $_=L$ on the subcalculus of MA (both the asynchronous and the synchronous version), enabling us to relate $_=L$ to structural congruence. We also present some (un)decidability results that are related to the above separation properties for AL: the undecidability of $_=L$ on MA and its decidability on the subcalculus.Comment: logical methods in computer science, 44 page

A hybrid type system for lock-freedom of mobile processes

We propose a type system for lock-freedom in the π-calculus, which guarantees that certain communications will eventually succeed. Distinguishing features of our type system are: it can verify lock-freedom of concurrent programs that have sophisticated recursive communication structures; it can be fully automated; it is hybrid, in that it combines a type system for lock-freedom with local reasoning about deadlockfreedom, termination, and confluence analyses. Moreover, the type system is parameterized by deadlock-freedom/termination/confluence analyses, so that any methods (e.g. type systems and model checking) can be used for those analyses. A lock-freedom analysis tool has been implemented based on the proposed type system, and tested for non-trivial programs

Unique Solutions of Contractions, CCS, and their HOL Formalisation

The unique solution of contractions is a proof technique for bisimilarity that overcomes certain syntactic constraints of Milner's "unique solution of equations" technique. The paper presents an overview of a rather comprehensive formalisation of the core of the theory of CCS in the HOL theorem prover (HOL4), with a focus towards the theory of unique solutions of contractions. (The formalisation consists of about 20,000 lines of proof scripts in Standard ML.) Some refinements of the theory itself are obtained. In particular we remove the constraints on summation, which must be weakly-guarded, by moving to rooted contraction, that is, the coarsest precongruence contained in the contraction preorder.Comment: In Proceedings EXPRESS/SOS 2018, arXiv:1808.0807

Expressing mobility in process algebras: first-order and higher-order paradigms

We study mobile systems, i.e. systems with a dynamically changing communication topology, from a process algebras point of view. Mobility can be introduced in process algebras by allowing names or terms to be transmitted. We distinguish these two approaches as first-order and higher-order. The major target of the thesis is the comparison between them. The prototypical calculus in the first-order paradigm is the π-calculus. By generalising its sort discipline we derive an w-order extension called Higher-Order π-calculus (HOπ). We show that such an extension does not add expressiveness to the π-calculus: Higher-order processes can be faithfully compiled down to first-order, and respecting the behavioural equivalence we adopted in the calculi. Such an equivalence is based on the notion of bisimulation, a fundamental concept of process algebras. Unfortunately, the standard definition of bisimulation is unsatisfactory in a higher-order calculus because it is over-discriminating. To overcome the problem, we propose barbed bisimulation. Its advantage is that it can be defined uniformly in different calculi because it only requires that the calculus possesses an interaction or reduction relation. As a test for barbed bisimulation, we show that in CCS and π-calculus, it allows us to recover the familiar bisimulation-based equivalences. We also give simpler characterisations of the equivalences utilised in HOπ. For this we exploit a special kind of agents called triggers, with which it is possible to reason fairly efficiently in a higher-order calculus notwithstanding the complexity of its transitions. Finally, we use the compilation from HOπ to π-calculus to investigate Milner'

Magnetic resonance fingerprinting con reti neurali a valori complessi

In questo documento cerco un metodo per migliorare le prestazioni del MRF (Magnetic Resonance Fingerprinting), una tecnica di risonanza magnetica quantitativa. Il problema è quello di diminuire il tempo di calcolo necessario per determinare i parametri tissutali relativi alla risonanza magnetica effettuata. Il metodo proposto è quello dell'utilizzo di reti neurali a valori complessi con input il segnale di risonanza magnetica e con output i valori relativi ai parametri che si vogliono studiare. Dopo aver chiarito il concetto di risonanza magnetica, di MRF ed i problemi ad essi associati, introduco le reti neurali: l'architettura, la dinamica e l'apprendimento relativi ad esse. Discuto a seguire i problemi relativi all'introduzione dei numeri complessi nel modello di rete neurale e anche i vantaggi che le reti neurali a valori complessi possono portare, non solo rispetto ai metodi tradizionali, ma anche rispetto a reti neurali a valori reali. Analizzo inoltre delle tecniche utili a migliorare la generalizzazione e rendere le reti neurali a valori complessi una soluzione ancora più concreta. Studio quindi i miglioramenti introdotti dagli ensemble di reti neurali e dall'applicazione di funzioni d'attivazione stocastiche, che introducono del rumore gaussiano all'interno del modello

pi-calculus, internal mobility, and agent-passing calculi

The $\pi$-calculus is a process algebra which originates from CCS and permits a natural modelling of mobility (i.e., dynamic reconfigurations of the process linkage) using communication of names. Previous research has shown that the $\pi$-calculus has much greater expressiveness than CCS, but also a much more complex mathematical theory. The primary goal of this work is to understand the reasons of this gap. Another goal is to compare the expressiveness of {\em \no} calculi, i.e., calculi like $\pi$-calculus where mobility is achieved via exchange of names, and that of {\em agent-passing calculi}, i.e., calculi where mobility is achieved via exchange of agents. We separate the mobility mechanisms of the \pic into two, respectively called {\em internal mobility} and {\em external mobility}. The study of the subcalculus which only uses internal mobility, called \pii, suggests that internal mobility is responsible for {much} of the expressiveness of the $\pi$-calculus, whereas external mobility is responsible for {much} of the semantic complications. A pleasant property of \pii  is the full symmetry between input and output constructs. Internal mobility is strongly related to agent-passing mobility. By imposing bounds on the order of the types of \pii and of the Higher-Order $\pi$-calculus \cite{San923} we define a hierarchy of name-passing calculi based on internal mobility and one of agent-passing calculi. We show that there is an exact correspondence, in terms of expressiveness, between the two hierarchies