Network-Conscious π-calculus – A Model of Pastry

AbstractA peer-to-peer (p2p) system provides the networking substrate for the execution of distributed applications. It is made of peers that interact over an overlay network. Overlay networks are highly dynamic, as peers can join and leave at any time. Traditional process calculi, such as π-calculus, CCS and others, seem inadequate to capture these kinds of networks, their routing mechanisms, and to verify their properties. In order to model network architecture in a more explicit way, in [Ugo Montanari and Matteo Sammartino. Network conscious π-calculus: A concurrent semantics. ENTCS, 286:291–306, 2012; Matteo Sammartino. A Network-Aware Process Calculus for Global Computing and its Categorical Framework. PhD thesis, University of Pisa, 2013. available at http://www.di.unipi.it/~sammarti/publications/thesis.pdf; Ugo Montanari and Matteo Sammartino. A network-conscious π-calculus and its coalgebraic semantics. Theor. Comput. Sci., 546:188–224, 2014] we have introduced the Network Conscious π-calculus (NCPi), an extension of the π-calculus with names representing network nodes and links. In [Ugo Montanari and Matteo Sammartino. A network–conscious π-calculus and its coalgebraic semantics. Theor. Comput. Sci., 546:188–224, 2014] (a simpler version of) NCPi has been equipped with a coalgebraic operational models, along the lines of Fiore-Turi presheaf-based approach [Marcelo P. Fiore and Daniele Turi. Semantics of name and value passing. In LICS 2001, pages 93–104. IEEE Computer Society, 2001], and with an equivalent History Dependent Automaton [Ugo Montanari and Marco Pistore. Structured coalgebras and minimal hd-automata for the π-calculus. Theor. Comput. Sci., 340(3):539–576, 2005], i.e., an (often) finite-state automaton suitable for verification. In this paper we first give a brief account of these results. Then, our contribution is the sketch of a NCPi representation of the p2p architecture Pastry. In particular, we give models of its overlay network and of a Distributed Hash Table built on top of it, and we give evidence of their correctness by proving convergence of routing mechanisms

A type system for counting instances of software components

We identify an abstract language for component software based on process algebra. Besides the usual operators for sequential, alternative and parallel composition, it has primitives for instantiating components and for deleting instances of components. We define an operational semantics for our language and give a type system in which types express quantitative information on the components involved in the execution of the expressions of the language. Included in this information is for each component the maximum number of instances that are simultaneously active during the execution of the expression. The type system is compositional by the novel use of ‘deficit types’. The type inference algorithm runs in time quadratic in the size of the input. We consider extensions of the language with loops and tail recursion, and with a scope mechanism. We illustrate the approach with some examples, one on UML diagram refinement and one on counting objects on the free store in C++

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