Bayesian network semantics for Petri nets

Recent work by the authors equips Petri occurrence nets (PN) with probability distributions which fully replace nondeterminism. To avoid the so-called confusion problem, the construction imposes additional causal dependencies which restrict choices within certain subnets called structural branching cells (s-cells). Bayesian nets (BN) are usually structured as partial orders where nodes define conditional probability distributions. In the paper, we unify the two structures in terms of Symmetric Monoidal Categories (SMC), so that we can apply to PN ordinary analysis techniques developed for BN. Interestingly, it turns out that PN which cannot be SMC-decomposed are exactly s-cells. This result confirms the importance for Petri nets of both SMC and s-cells.Fil: Bruni, Roberto. Università degli Studi di Pisa; ItaliaFil: Melgratti, Hernan Claudio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigación en Ciencias de la Computación. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigación en Ciencias de la Computación; ArgentinaFil: Montanari, Ugo. Università degli Studi di Pisa; Itali

Reversing place transition nets

Petri nets are a well-known model of concurrency and provide an ideal setting for the study of fundamental aspects in concurrent systems. Despite their simplicity, they still lack a satisfactory causally reversible semantics. We develop such semantics for Place/Transitions Petri nets (P/T nets) based on two observations. Firstly, a net that explicitly expresses causality and conflict among events, for example an occurrence net, can be straightforwardly reversed by adding a reverse transition for each of its forward transitions. Secondly, given a P/T net the standard unfolding construction associates with it an occurrence net that preserves all of its computation. Consequently, the reversible semantics of a P/T net can be obtained as the reversible semantics of its unfolding. We show that such reversible behaviour can be expressed as a finite net whose tokens are coloured by causal histories. Colours in our encoding resemble the causal memories that are typical in reversible process calculi.Fil: Melgratti, Hernan Claudio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigación en Ciencias de la Computación. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigación en Ciencias de la Computación; ArgentinaFil: Mezzina, Claudio Antares. Università Degli Studi Di Urbino Carlo Bo; ItaliaFil: Ulidowski, And Irek. University of Leicester; Reino Unid

Concurrency and Probability: Removing Confusion, Compositionally

Assigning a satisfactory truly concurrent semantics to Petri nets with confusion and distributed decisions is a long standing problem, especially if one wants to resolve decisions by drawing from some probability distribution. Here we propose a general solution to this problem based on a recursive, static decomposition of (occurrence) nets in loci of decision, called structural branching cells (s-cells). Each s-cell exposes a set of alternatives, called transactions. Our solution transforms a given Petri net, possibly with confusion, into another net whose transitions are the transactions of the s-cells and whose places are those of the original net, with some auxiliary nodes for bookkeeping. The resulting net is confusion-free by construction, and thus conflicting alternatives can be equipped with probabilistic choices, while nonintersecting alternatives are purely concurrent and their probability distributions are independent. The validity of the construction is witnessed by a tight correspondence with the recursively stopped configurations of Abbes and Benveniste. Some advantages of our approach are that: i) s-cells are defined statically and locally in a compositional way; ii) our resulting nets faithfully account for concurrency.Fil: Bruni, Roberto Hector. Università degli Studi di Pisa; ItaliaFil: Melgratti, Hernan Claudio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigación en Ciencias de la Computación. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigación en Ciencias de la Computación; ArgentinaFil: Montanari, Ugo. Università degli Studi di Pisa; Itali

Chaperone contracts for higher-order sessions

Contracts have proved to be an effective mechanism that helps developers in identifying those modules of a program that violate the contracts of the functions and objects they use. In recent years, sessions have established as a key mechanism for realizing inter-module communications in concurrent programs. Just like values flow into or out of a function or object, messages are sent on, and received from, a session endpoint. Unlike conventional functions and objects, however, the kind, direction, and properties of messages exchanged in a session may vary over time, as the session progresses. This feature of sessions calls for contracts that evolve along with the session they describe.In this work, we extend to sessions the notion of chaperone contract (roughly, a contract that applies to a mutable object) and investigate the ramifications of contract monitoring in a higher-order language that features sessions. We give a characterization of correct module, one that honors the contracts of the sessions it uses, and prove a blame theorem. Guided by the calculus, we describe a lightweight implementation of monitored sessions as an OCaml module with which programmers can benefit from static session type checking and dynamic contract monitoring using an off-the-shelf version of OCaml.Fil: Melgratti, Hernan Claudio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigación En Ciencias de la Computación. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigación En Ciencias de la Computacion; ArgentinaFil: Padovani, Luca. Università di Torino; Itali

A formal analysis of the global sequence protocol

The Global Sequence Protocol (GSP) is an operational model for replicated data stores, in which updates propagate asynchronously. We introduce the GSP-calculus as a formal model for GSP. We give a formal account for its proposed implementation, which addresses communication failures and compact representation of data, and use simulation to prove that the implementation is correct. Then, we use the GSP-calculus to reason about execution histories and prove ordering guarantees, such as read my writes, monotonic reads, causality and consistent prefix. We also prove that GSP extended with synchronous updates provides strong consistency guarantees.Fil: Melgratti, Hernan Claudio. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; ArgentinaFil: Roldán, Christian Hugo. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentin

Behaviour, Interaction and Dynamics

The growth and diffusion of reconfigurable and adaptive sys- tems motivate the foundational study of models of software connectors that can evolve dynamically, as opposed to the better understood no- tion of static connectors. In this paper we investigate the interplay of behaviour, interaction and dynamics in the context of the BIP com- ponent framework, here denoted BI(P), as we disregard priorities. We introduce two extensions of BIP: 1) reconfigurable BI(P) allows to re- configure the set of admissible interactions, while preserving the set of interacting components; 2) dynamic BI(P) allows to spawn new compo- nents and interactions during execution. Our main technical results show that reconfigurable BI(P) is as expressive as BI(P), while dynamic BI(P) allows to deal with infinite state systems. Still, we show that reachability remains decidable for dynamic BI(P).Fil: Bruni, Roberto. Università degli Studi di Pisa; ItaliaFil: Melgratti, Hernan Claudio. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Montanari, Ugo. Università degli Studi di Pisa; Itali

A normal form for stateful connectors

In this paper we consider a calculus of connectors that allows for the most general combination of synchronisation, non-determinism and buffering. According to previous results, this calculus is tightly related to a flavour of Petri nets with interfaces for composition, called Petri nets with boundaries. The calculus and the net version are equipped with equivalent bisimilarity semantics. Also the buffers (the net places) can be one-place (C/E nets) or with unlimited capacity (P/T nets). In the paper we investigate the idea of finding normal form representations for terms of this calculus, in the sense that equivalent (bisimilar) terms should have the same (isomorphic) normal form. We show that this is possible for finite state terms. The result is obtained by computing the minimal marking graph (when finite) for the net with boundaries corresponding to the given term, and reconstructing from it a canonical net and a canonical term.Fil: Bruni, Roberto. Università degli Studi di Pisa; ItaliaFil: Melgratti, Hernan Claudio. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria; ArgentinaFil: Montanari, Ugo. Università degli Studi di Pisa; Itali

A categorical account of replicated data types

Replicated Data Types (rdts) have been introduced as a suitable abstraction for dealing with weakly consistent data stores, which may (temporarily) expose multiple, inconsistent views of their state. In the literature, rdts are commonly specified in terms of two relations: visibility, which accounts for the different views that a store may have, and arbitration, which states the logical order imposed on the operations executed over the store. Different flavours, e.g., operational, axiomatic and functional, have recently been proposed for the specification of rdts. In this work, we propose an algebraic characterisation of rdt specifications. We define categories of visibility relations and arbitrations, show the existence of relevant limits and colimits, and characterize rdt specifications as functors between such categories that preserve these additional structures.Fil: Gadducci, Fabio. Università degli Studi di Pisa; ItaliaFil: Melgratti, Hernan Claudio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigación en Ciencias de la Computación. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigación en Ciencias de la Computación; ArgentinaFil: Roldán, Christian Hugo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigación en Ciencias de la Computación. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigación en Ciencias de la Computación; ArgentinaFil: Sammartino, Matteo. University College London; Estados Unido