234 research outputs found
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
BigraphER: rewriting and analysis engine for bigraphs
BigraphER is a suite of open-source tools providing an effi-
cient 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
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
Spatial Logics for Bigraphs
Bigraphs are emerging as an interesting model for concurrent calculi, like CCS, pi-calculus, and Petri nets. Bigraphs are built orthogonally on two structures: a hierarchical place graph for locations and a link (hyper-)graph for connections. With the aim of describing bigraphical structures, we introduce a general framework for logics whose terms represent arrows in monoidal categories. We then instantiate the framework to bigraphical structures and obtain a logic that is a natural composition of a place graph logic and a link graph logic. We explore the concepts of separation and sharing in these logics and we prove that they generalise some known spatial logics for trees, graphs and tree contexts
Bigraphical Logics for XML
Bigraphs have been recently proposed as a meta-model for global computing resources; they are built orthogonally on two structures: a hierarchical ‘place’ graph for locations and a ‘link’ (hyper-)graph for connections. XML is now the standard meta-language for the data exchange and storage on the web. In this paper we address the similarities between bigraphs and XML and we propose bigraphs as a rich model for XML (and XML contexts). Building on this idea we proceed by investigating how the recently proposed logic of BiLog can be instantiated to describe, query and reason about web data (and web contexts)
Variable binding, symmetric monoidal closed theories, and bigraphs
This paper investigates the use of symmetric monoidal closed (SMC) structure
for representing syntax with variable binding, in particular for languages with
linear aspects. In our setting, one first specifies an SMC theory T, which may
express binding operations, in a way reminiscent from higher-order abstract
syntax. This theory generates an SMC category S(T) whose morphisms are, in a
sense, terms in the desired syntax. We apply our approach to Jensen and
Milner's (abstract binding) bigraphs, which are linear w.r.t. processes. This
leads to an alternative category of bigraphs, which we compare to the original.Comment: An introduction to two more technical previous preprints. Accepted at
Concur '0
FollowMe: A Bigraphical Approach
In this paper we illustrate the use of modelling techniques using bigraphs to specify and refine elementary aspects of the FollowMe framework. This framework provides the seamless migration of bi-directional user interfaces for users as they navigate between zones within an intelligent environment
BiLog - A Framework for Structural Logics (talk)
Talk given at Forum on Separation Logics, Cambridge 14.03.0
Distributed execution of bigraphical reactive systems
The bigraph embedding problem is crucial for many results and tools about
bigraphs and bigraphical reactive systems (BRS). Current algorithms for
computing bigraphical embeddings are centralized, i.e. designed to run locally
with a complete view of the guest and host bigraphs. In order to deal with
large bigraphs, and to parallelize reactions, we present a decentralized
algorithm, which distributes both state and computation over several concurrent
processes. This allows for distributed, parallel simulations where
non-interfering reactions can be carried out concurrently; nevertheless, even
in the worst case the complexity of this distributed algorithm is no worse than
that of a centralized algorithm
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