Published in Volume XX, 2010, pages 53-96

Authors: R. Bruni, F. Gadducci, and A. Lluch Lafuente

Abstract

We define an algebraic theory of hierarchical graphs, whose axioms
characterise graph isomorphism: two terms are equated exactly when
they represent the same graph. Our algebra can be understood as
a high-level language for describing graphs with a node-sharing, embedding structure, and it is then well suited for defining graphical
representations of software models where nesting and linking are key
aspects. In particular, we propose the use of our graph formalism as a
convenient way to describe configurations in process calculi equipped
with inherently hierarchical features such as sessions, locations, transactions, membranes or ambients. The graph syntax can be seen as an
intermediate representation language, that facilitates the encodings of
algebraic specifications, since it provides primitives for nesting, name restriction and parallel composition. In addition, proving soundness and correctness of an encoding (i.e. proving that structurally equivalent processes are mapped to isomorphic graphs) becomes easier as it can be done by induction over the graph syntax.

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Bibtex

@article{sacscuza:bruni2010aaohgaiatse,
  title={An Algebra of Hierarchical Graphs and its Application to Structural Encoding},
  author={R. Bruni and F. Gadducci and A. Lluch Lafuente},
  journal={Scientific Annals of Computer Science},
  volume={20},
  organization={``A.I. Cuza'' University, Iasi, Romania},
  year={2010},
  pages={53--96},
  publisher={``A.I. Cuza'' University Press}
}