22 research outputs found
Axioms for bigraphical structure
This paper axiomatises the structure of bigraphs, and proves that the resulting theory is complete. Bigraphs are graphs with double structure, representing locality and connectivity. They have been shown to represent dynamic theories for the #-calculus, mobile ambients and Petri nets, in a way that is faithful to each of those models of discrete behaviour. While the main purpose of bigraphs is to understand mobile systems, a prerequisite for this understanding is a well-behaved theory of the structure of states in such systems. The algebra of bigraph structure is surprisingly simple, as the paper demonstrates; this is because bigraphs treat locality and connectivity orthogonall
The Algebra of Directed Acyclic Graphs
We give an algebraic presentation of directed acyclic graph structure,
introducing a symmetric monoidal equational theory whose free PROP we
characterise as that of finite abstract dags with input/output interfaces. Our
development provides an initial-algebra semantics for dag structure
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)
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
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
Verifying bigraphical models of architectural reconfigurations
ARCHERY is an architectural description language for modelling and reasoning about distributed, heterogeneous and dynamically reconfigurable systems. This paper proposes a structural semantics for ARCHERY, and a method for deriving labelled transition systems (LTS) in which states and transitions represent configurations and reconfiguration operations, respectively. Architectures are modelled by bigraphs and their dynamics by parametric reaction rules. The resulting LTSs can be regarded as Kripke frames, appropriate for verifying reconfiguration constraints over architectural patterns expressed in a modal logic. The derivation method proposed here applies Leifer's approach twice, and combines the results of each application to obtain a label representing a reconfiguration operation and its actual parameters. Labels obtained in this way are minimal and yield LTSs in which bisimulation is a congruence.FC
A new graphical calculus of proofs
We offer a simple graphical representation for proofs of intuitionistic
logic, which is inspired by proof nets and interaction nets (two formalisms
originating in linear logic). This graphical calculus of proofs inherits good
features from each, but is not constrained by them. By the Curry-Howard
isomorphism, the representation applies equally to the lambda calculus,
offering an alternative diagrammatic representation of functional computations.Comment: In Proceedings TERMGRAPH 2011, arXiv:1102.226
An Algebra for Directed Bigraphs
We study the algebraic structure of directed bigraphs, a bigraphical model of computations with locations, connections and resources previously introduced as a unifying generalization of other variants of bigraphs. We give a sound and complete axiomatization of the (pre)category of directed bigraphs. Using this axiomatization, we give an adequate encoding of the Fusion calculus, showing the utility of the added directnes
Bigraphical Refinement
We propose a mechanism for the vertical refinement of bigraphical reactive
systems, based upon a mechanism for limiting observations and utilising the
underlying categorical structure of bigraphs. We present a motivating example
to demonstrate that the proposed notion of refinement is sensible with respect
to the theory of bigraphical reactive systems; and we propose a sufficient
condition for guaranteeing the existence of a safety-preserving vertical
refinement. We postulate the existence of a complimentary notion of horizontal
refinement for bigraphical agents, and finally we discuss the connection of
this work to the general refinement of Reeves and Streader.Comment: In Proceedings Refine 2011, arXiv:1106.348