Matteo Sammartino

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-Plotkins 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.

Network Conscious π-calculus: A Concurrent 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 [Openflow foundation website, http://www.openflow.org/], where programs are allowed to manipulate the infrastructure. In this paper we present a network conscious, proper extension of the @p-calculus: we add connector names and the primitives to handle them, and we provide a concurrent semantics. The extension to connector names is natural and seamless, since they are handled in full analogy with ordinary names. Our observations are multisets of routing paths through which sent and received data are transported. However, restricted connector names do not appear in the observations, which thus can possibly be as abstract as in the @p-calculus. Finally, we show that bisimilarity is a congruence, and this property holds also for the concurrent version of the @p-calculus.

Learning nominal automata

We present an Angluin-style algorithm to learn nominal automata, which are acceptors of languages over infinite (structured) alphabets. The abstract approach we take allows us to seamlessly extend known variations of the algorithm to this new setting. In particular we can learn a subclass of nominal non-deterministic automata. An implementation using a recently developed Haskell library for nominal computation is provided for preliminary experiments.

Reconfigurable and Software-Defined Networks of Connectors and Components

The diffusion of adaptive systems motivate the study of models of software entities whose interaction capabilities can evolve dynamically. In this paper we overview the contributions in the ASCENS project in the area of software defined networks and of reconfigurable connectors. In particular we highlight: (i) the definition of the Network-conscious pi-calculus and its use in the modeling and verification of the PASTRY protocol, and (ii) the mutual correspondence between different frameworks for defining networks of connectors together with two suitable enhancements for addressing dynamically changing systems.

From Local to Global Knowledge and Back

Two forms of knowledge are considered: declarative and procedural. The former is easy to extend but it is equipped with expensive deduction mechanisms, while the latter is efficiently executable but it can hardly anticipate all the special cases. In the first part of this chapter (Sections 2 and 3), we first define a syntactic representation of Soft Constraint Satisfaction Problems (SCSPs), which allows us to express dynamic programming (DP) strategies. For the e-mobility case study of ASCENS, we use Soft Constraint Logic Programming (SCLP) to program (in CIAO Prolog) and solve local optimization problems of single electric vehicles. Then we treat the global optimization problem of finding optimal parking spots for all the cars. We provide: (i) a Java orchestrator for the coordination of local SCLP optimizations; and (ii) a DP algorithm, which corresponds to a local to global propagation and back. In the second part of this chapter (Section 4) we assume that different subjects are entitled to decide. The case study concerns a smart grid model where various prosumers (producers-consumers) negotiate (in real time, according to the DEZENT approach) the cost of the exchanged energy. Then each consumer tries to plan an optimal consumption profile (computed via DP) where (s)he uses less energy when it is expensive and more energy when it is cheap, conversely for a producer. Finally, the notion of an aggregator is introduced, whose aim is to sell flexibility to the market.

Revisiting causality, coalgebraically

In this paper we recast the classical Darondeau–Degano’s causal semantics of concurrency in a coalgebraic setting, where we derive a compact model. Our construction is inspired by the one of Montanari and Pistore yielding causal automata, but we show that it is instance of an existing categorical framework for modeling the semantics of nominal calculi, whose relevance is further demonstrated. The key idea is to represent events as names, and the occurrence of a new event as name generation. We model causal semantics as a coalgebra over a presheaf, along the lines of the Fiore–Turi approach to the semantics of nominal calculi. More specifically, we take a suitable category of finite posets, representing causal relations over events, and we equip it with an endofunctor that allocates new events and relates them to their causes. Presheaves over this category express the relationship between processes and causal relations among the processes’ events. We use the allocation operator to define a category of well-behaved coalgebras: it models the occurrence of a new event along each transition. Then we turn the causal transition relation into a coalgebra in this category, where labels only exhibit maximal events with respect to the source states’ poset, and we show that its bisimilarity is essentially Darondeau–Degano’s strong causal bisimilarity. This coalgebra is still infinite-state, but we exploit the equivalence between coalgebras over a class of presheaves and History Dependent automata to derive a compact representation, where states only retain the poset of the most recent events for each atomic subprocess, and are isomorphic up to order-preserving permutations. Remarkably, this reduction of states is automatically performed along the equivalence.

A coalgebraic semantics for causality in Petri nets

In this paper we revisit some pioneering eorts to equip Petri nets with compact operational models for expressing causality. The models we propose have a bisimilarity relation and a minimal representative for each equivalence class, and they can be fully explained as coalgebras on a presheaf category on an index category of partial orders. First, we provide a set-theoretic model in the form of a a causal case graph, that is a labeled transition system where states and transitions represent markings and rings of the net, respectively, and are equipped with causal information. Most importantly, each state has a poset representing causal dependencies among past events. Our rst result shows the correspondence with behavior structure semantics as proposed by Trakhtenbrot and Rabinovich. Causal case graphs may be innitely-branchi ng and have innitely many states, but we show how they can be rened to get an equivalent nitely-branching model. In it, states only keep the most recent causes for each token, are up to isomorphism, and are equipped with a symmetry, i.e., a group of poset isomorphisms. Symmetries are essential for the existence of a minimal, often nite-state, model. This rst part requires no knowledge of category theory. The next step is constructing a coalgebraic model. We exploit the fact that events can be represented as names, and event generation as name generation. Thus we can apply the Fiore-Turi framework, where the semantics of nominal calculi are modeled as coalgebras over presheaves. We model causal relations as a suitable category of posets with action labels, and generation of new events with causal dependencies as an endofunctor on this category. Presheaves indexed by labeled posets represent the functorial association between states and their causal information. Then we dene a well-behaved category of coalgebras. Our coalgebraic model is still innite-state, but we exploit the equivalence between coalgebras over a class of presheaves and History Dependent automata to derive a compact representation, which is equivalent to our set-theoretical compact model. Remarkably, state reduction is automatically performed along the equivalence.

Dynamic Programming on Nominal Graphs

Many optimization problems can be naturally represented as (hyper) graphs, where vertices correspond to variables and edges to tasks, whose cost depends on the values of the adjacent variables. Capitalizing on the structure of the graph, suitable dynamic programming strategies can select certain orders of evaluation of the variables which guarantee to reach both an optimal solution and a minimal size of the tables computed in the optimization process. In this paper we introduce a simple algebraic specification with parallel composition and restriction whose terms up to structural axioms are the graphs mentioned above. In addition, free (unrestricted) vertices are labelled with variables, and the specification includes operations of name permutation with finite support. We show a correspondence between the well-known tree decompositions of graphs and our terms. If an axiom of scope extension is dropped, several (hierarchical) terms actually correspond to the same graph. A suitable graphical structure can be found, corresponding to every hierarchical term. Evaluating such a graphical structure in some target algebra yields a dynamic programming strategy. If the target algebra satisfies the scope extension axiom, then the result does not depend on the particular structure, but only on the original graph. We apply our approach to the parking optimization problem developed in the ASCENS e-mobility case study, in collaboration with Volkswagen. Dynamic programming evaluations are particularly interesting for autonomic systems, where actual behavior often consists of propagating local knowledge to obtain global knowledge and getting it back for local decisions.

Network-Conscious π-calculus - A Model of Pastry

A 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 Class of Automata for the Verification of Infinite, Resource-Allocating Behaviours

Process calculi for service-oriented computing often feature generation of fresh resources. So-called nominal automata have been studied both as semantic models for such calculi, and as acceptors of languages of finite words over infinite alphabets. In this paper we investigate nominal automata that accept infinite words. These automata are a generalisation of deterministic Muller automata to the setting of nominal sets. We prove decidability of complement, union, intersection, emptiness and equivalence, and determinacy by ultimately periodic words. The key to obtain such results is to use finite representations of the (otherwise infinite-state) defined class of automata. The definition of such operations enables model checking of process calculi featuring infinite behaviours, and resource allocation, to be implemented using classical automata-theoretic methods.