455 research outputs found

    Graph Algebras for Bigraphs

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    Binding bigraphs are a graphical formalism intended to be a meta-model for mobile, concurrent and communicating systems. In this paper we present an algebra of typed graph terms which correspond precisely to binding bigraphs over a given signature. As particular cases, pure bigraphs and local bigraphs are described by two sublanguages which can be given a simple syntactic characterization. Moreover, we give a formal connection between these languages and Synchronized Hyperedge Replacement algebras and the hierarchical graphs used in Architectural Design Rewriting. This allows to transfer results and constructions among formalisms which have been developed independently, e.g., the systematic definition of congruent bisimulations for SHR graphs via the IPO construction

    Algebras for Tree Decomposable Graphs

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    Complex problems can be sometimes solved efficiently via recursive decomposition strategies. In this line, the tree decomposition approach equips problems modelled as graphs with tree-like parsing structures. Following Milner’s flowgraph algebra, in a previous paper two of the authors introduced a strong network algebra to represent open graphs (up to isomorphism), so that homomorphic properties of open graphs can be computed via structural recursion. This paper extends this graphical-algebraic foundation to tree decomposable graphs. The correspondence is shown: (i) on the algebraic side by a loose network algebra, which relaxes the restriction reordering and scope extension axioms of the strong one; and (ii) on the graphical side by Milner’s binding bigraphs, and elementary tree decompositions. Conveniently, an interpreted loose algebra gives the evaluation complexity of each graph decomposition. As a key contribution, we apply our results to dynamic programming (DP). The initial statement of the problem is transformed into a term (this is the secondary optimisation problem of DP). Noting that when the scope extension axiom is applied to reduce the scope of the restriction, then also the complexity is reduced (or not changed), only so-called canonical terms (in the loose algebra) are considered. Then, the canonical term is evaluated obtaining a solution which is locally optimal for complexity. Finding a global optimum remains an NP-hard problem

    A graph semantics for a variant of the ambient calculus more adequate for modeling SOC

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    In this paper we present a graph semantics of a variant of the well known ambient calculus. The main change of our variant is to extract the mobility commands of the original calculus from the ambient topology. Similar to a previous work of ours, we prove that our encoding have good properties. We strongly believe that this variant would allow us to integrate our graph semantics of our mobile calculus with previous work of us in service oriented computing (SOC). Basically, our work on SOC develops a new graph transformation system which we call temporal symbolic graphs. This new graph formalism is used to give semantics to a design language for SOC developed in an european project, but it could also be used in connection with other approaches for modeling or specifying service systems.Postprint (published version

    String Diagrams for λ\lambda-calculi and Functional Computation

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    This tutorial gives an advanced introduction to string diagrams and graph languages for higher-order computation. The subject matter develops in a principled way, starting from the two dimensional syntax of key categorical concepts such as functors, adjunctions, and strictification, and leading up to Cartesian Closed Categories, the core mathematical model of the lambda calculus and of functional programming languages. This methodology inverts the usual approach of proceeding from syntax to a categorical interpretation, by rationally reconstructing a syntax from the categorical model. The result is a graph syntax -- more precisely, a hierarchical hypergraph syntax -- which in many ways is shown to be an improvement over the conventional linear term syntax. The rest of the tutorial focuses on applications of interest to programming languages: operational semantics, general frameworks for type inference, and complex whole-program transformations such as closure conversion and automatic differentiation

    Graphs in molecular biology

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    Graph theoretical concepts are useful for the description and analysis of interactions and relationships in biological systems. We give a brief introduction into some of the concepts and their areas of application in molecular biology. We discuss software that is available through the Bioconductor project and present a simple example application to the integration of a protein-protein interaction and a co-expression network
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