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An Algebra of Hierarchical Graphs and its Application to Structural Encoding
, 2010
"... 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 highlevel language for describing graphs with a nodesharing, embedding structure, and it is then w ..."
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Cited by 4 (1 self)
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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 highlevel language for describing graphs with a nodesharing, 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.
Adhesivity is not enough: Local ChurchRosser revisited
"... Adhesive categories provide an abstract setting for the doublepushout approach to rewriting, generalising classical approaches to graph transformation. Fundamental results about parallelism and confluence, including the local ChurchRosser theorem, can be proven in adhesive categories, provided th ..."
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Cited by 2 (0 self)
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Adhesive categories provide an abstract setting for the doublepushout approach to rewriting, generalising classical approaches to graph transformation. Fundamental results about parallelism and confluence, including the local ChurchRosser theorem, can be proven in adhesive categories, provided that one restricts to linear rules. We identify a class of categories, including most adhesive categories used in rewriting, where those same results can be proven in the presence of rules that are merely leftlinear, i.e., rules which can merge different parts of a rewritten object. Such rules naturally emerge, e.g., when using graphical encodings for modelling the operational semantics of process calculi.
Under consideration for publication in Math. Struct. in Comp. Science Concurrency Can’t Be Observed, Asynchronously †
, 2012
"... The paper is devoted to an analysis of the concurrent features of asynchronous systems. A preliminary step is represented by the introduction of a noninterleaving extension of barbed equivalence. This notion is then exploited in order to prove that concurrency cannot be observed through asynchronou ..."
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The paper is devoted to an analysis of the concurrent features of asynchronous systems. A preliminary step is represented by the introduction of a noninterleaving extension of barbed equivalence. This notion is then exploited in order to prove that concurrency cannot be observed through asynchronous interactions, i.e., that the interleaving and concurrent versions of a suitable asynchronous weak equivalence actually coincide. The theory is validated on some case studies, related to nominal calculi (πcalculus) and visual specification formalisms (Petri nets). Additionally, we prove that a class of systems which are (outputbuffered) asynchronous according to a characterisation previously proposed in the literature falls into our theory.