Michele Sevegnani

Bigraphs with sharing

Bigraphical Reactive Systems (BRS) were designed by Milner as a universal formalism for modelling systems that evolve in time, locality, co-locality and connectivity. But the underlying model of location (the place graph) is a forest, which means there is no straightforward representation of locations that can overlap or intersect. This occurs in many domains, for example in wireless signalling, social interactions and audio communications. Here, we define bigraphs with sharing, which solves this problem by an extension of the basic formalism: we define the place graph as a directed acyclic graph, thus allowing a natural representation of overlapping or intersecting locations. We give a complete presentation of the theory of bigraphs with sharing, including a categorical semantics, algebraic properties, and several essential procedures for computation: bigraph with sharing matching, a SAT encoding of matching, and checking a fragment of the logic BiLog. We show that matching is an instance of the NP-complete sub-graph isomorphism problem and our approach based on a SAT encoding is also efficient for standard bigraphs. We give an overview of BigraphER (Bigraph Evaluator & Rewriting), an efficient implementation of bigraphs with sharing that provides manipulation, simulation and visualisation. The matching engine is based on the SAT encoding of the matching algorithm. Examples from the 802.11 CSMA/CA RTS/CTS protocol and a network management support system illustrate the applicability of the new theory.

Modelling IEEE 802.11 CSMA/CA RTS/CTS with stochastic bigraphs with sharing

Stochastic bigraphical reactive systems (SBRS) is a recent formalism for modelling systems that evolve in time and space. However, the underlying spatial model is based on sets of trees and thus cannot represent spatial locations that are shared among several entities in a simple or intuitive way. We adopt an extension of the formalism, SBRS with sharing, in which the topology is modelled by a directed acyclic graph structure. We give an overview of SBRS with sharing, we extend it with rule priorities, and then use it to develop a model of the 802.11 CSMA/CA RTS/CTS protocol with exponential backoff, for an arbitrary network topology with possibly overlapping signals. The model uses sharing to model overlapping connectedness areas, instantaneous prioritised rules for deterministic computations, and stochastic rules with exponential reaction rates to model constant and uniformly distributed timeouts and constant transmission times. Equivalence classes of model states modulo instantaneous reactions yield states in a CTMC that can be analysed using the model checker PRISM. We illustrate the model on a simple example wireless network with three overlapping signals and we present some example quantitative properties.

Real-time verification of wireless home networks using bigraphs with sharing

Home wireless networks are difficult to manage and comprehend because of evolving locality, co-locality, connectivity and interaction. We define formal models of home wireless network infrastructure and policies and investigate how they can be used in a network management system designed to provide user-oriented support. We model spatial and temporal behaviour of network interactions and user-initiated network policies and define an online framework for generation of models from network and user-initiated events. The models are expressed in an extension to Milner?s bigraphical reactive systems. Analysis of the models is carried out in real-time by a bespoke bigraph reasoning system based on checking predicates, which is encoded as bigraph matching. Real-time model generation and analysis is implemented on the experimental Homework system router and trialled with synthetic and actual network data.

Process algebra for event-driven runtime verification: a case study of wireless network management

Runtime verification is analysis based on information extracted from a running system. Traditionally this involves reasoning about system states, for example using trace predicates. We have been investigating runtime verification for event-driven systems and in that context we propose a higher level of abstraction can be useful, namely reasoning at the level of user-perceived system events. And when considering events, then the natural formalism for verification is a form of process algebra. We employ a universal process algebra that encapsulates both dynamic and spatial behaviour, based on Robin Milners bigraphs [1]. Our models are an extension of his bigraphical reactive systems. These consist of a set of bigraphs that describe spatial and communication relationships, and a set of bigraphical reaction rules that define how bigraphs can evolve over time. We have extended the basic formalism to bigraphical reactive systems with sharing [2], to allow for spatial locations that can overlap. In this talk we present a case study involving wireless home network management and the automatic generation of bigraphical models, and their analysis, in real-time. Wireless home networking is chosen as our case study because it is notoriously difficult to install and manage, especially for non-expert users. The Homework network management system [4] has been designed to provide user-oriented support in home wireless local area network (WLAN) environments. The Homework user interface includes drag and drop, comic-strip style interaction for users, and the information plane uses a stream database to record (raw and derived) events. Events include network behaviours such as detecting that a new machine has joined the network, resulting in new links and granting a DCHP lease, and user-intiated behaviours such as enforcing or dropping a policy. Policies forbid or allow access control; for example, a policy might block UDP and TCP traffic from a given site. All network and policy events (simple and derived) are recorded as a stream of tuples in the stream database. This part of the management system is illustrated in the left hand side of Figure 1.

On Lions, Impala, and Bigraphs: Modelling Interactions in Physical/Virtual Spaces

While HCI has a long tradition of formally modelling task-based interactions with graphical user interfaces, there has been less progress in modelling emerging ubiquitous computing systems due in large part to their highly contextual nature and dependence on unreliable sensing systems. We present an exploration of modelling an example ubiquitous system, the Savannah game, using the mathematical formalism of bigraphs, which are based on a universal process algebra that encapsulates both dynamic and spatial behaviour of autonomous agents that interact and move among each other, or within each other. We establish a modelling approach based on four perspectives on ubiquitous systems—Computational, Physical, Human, and Technology—and explore how these interact with one another. We show how our model explains observed inconsistencies in user trials of Savannah, and then, how formal analysis reveals an incompleteness in design and guides extensions of the model and/or possible system re-design to resolve this.

BigraphER: Rewriting and Analysis Engine for Bigraphs

BigraphER is a suite of open-source tools providing an efficient implementation of rewriting, simulation, and visualisation for bigraphs, a universal formalism for modelling interacting systems that evolve in time and space and first introduced by Milner. BigraphER consists of an OCaml library that provides programming interfaces for the manipulation of bigraphs, their constituents and reaction rules, and a command-line tool capable of simulating Bigraphical Reactive Systems (BRSs) and computing their transition systems. Other features are native support for both bigraphs and bigraphs with sharing, stochastic reaction rules, rule priorities, instantiation maps, parameterised controls, predicate checking, graphical output and integration with the probabilistic model checker PRISM.

Do I Need to Fix a Failed Component Now, or Can I Wait Until Tomorrow?

We investigate how predictive event-based modelling can inform operational decision making in complex systems with component failures. By relating the status of components to service availability, and using stochastic temporal logic reasoning, we quantify the risk of service failure now, and in the future, after a given elapsed time. Decisions can then be taken according to those risks. We demonstrate the approach through application to an industrial case study system in which component failures are sensed and monitored. The system has been deployed for some time. A novel aspect is we calibrate the model(s) according to inferences over historical field data, thus the results of our reasoning can inform decision making in the actual deployed system.