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Observing reductions in nominal calculi via a graphical encoding of processes
 Processes, terms and cycles (Klop Festschrift), volume 3838 of LNCS
"... Abstract. The paper introduces a novel approach to the synthesis of labelled transition systems for calculi with name mobility. The proposal is based on a graphical encoding: Each process is mapped into a (ranked) graph, such that the denotation is fully abstract with respect to the usual structural ..."
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Abstract. The paper introduces a novel approach to the synthesis of labelled transition systems for calculi with name mobility. The proposal is based on a graphical encoding: Each process is mapped into a (ranked) graph, such that the denotation is fully abstract with respect to the usual structural congruence (i.e., two processes are equivalent exactly when the corresponding encodings yield the same graph). Ranked graphs are naturally equipped with a few algebraic operations, and they are proved to form a suitable (bi)category of cospans. Then, as proved by Sassone and Sobocinski, the synthesis mechanism based on relative pushout, originally proposed by Milner and Leifer, can be applied. The resulting labelled transition system has ranked graphs as both states and labels, and it induces on (encodings of) processes an observational equivalence that is reminiscent of early bisimilarity.
On the Construction of Sorted Reactive Systems
 IN PROCEEDINGS OF CONCUR’08, LNCS
, 2008
"... We develop a theory of sorted bigraphical reactive systems. Every application of bigraphs in the literature has required an extension, a sorting, of pure bigraphs. In turn, every such application has required a redevelopment of the theory of pure bigraphical reactive systems for the sorting at hand. ..."
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We develop a theory of sorted bigraphical reactive systems. Every application of bigraphs in the literature has required an extension, a sorting, of pure bigraphs. In turn, every such application has required a redevelopment of the theory of pure bigraphical reactive systems for the sorting at hand. Here we present a general construction of sortings. The constructed sortings always sustain the behavioural theory of pure bigraphs (in a precise sense), thus obviating the need to redevelop that theory for each new application. As an example, we recover Milner’s local bigraphs as a sorting on pure bigraphs. Technically, we give our construction for ordinary reactive systems, then lift it to bigraphical reactive systems. As such, we give also a construction of sortings for ordinary reactive systems. This construction is an improvement over previous attempts in that it produces smaller and much more natural sortings, as witnessed by our recovery of local bigraphs as a sorting.
Toposes are adhesive
 In International Conference on Graph Tranformation, icgt’06, volume 4178 of Lect. Notes Comput. Sc
, 2006
"... Abstract. Adhesive categories have recently been proposed as a categorical foundation for facets of the theory of graph transformation, and have also been used to study techniques from process algebra for reasoning about concurrency. Here we continue our study of adhesive categories by showing that ..."
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Abstract. Adhesive categories have recently been proposed as a categorical foundation for facets of the theory of graph transformation, and have also been used to study techniques from process algebra for reasoning about concurrency. Here we continue our study of adhesive categories by showing that toposes are adhesive. The proof relies on exploiting the relationship between adhesive categories, Brown and Janelidze’s work on generalised van Kampen theorems as well as Grothendieck’s theory of descent.
On the Use of Behavioural Equivalences for Web Services’ Development
, 2008
"... Web services are emerging as a promising technology for the development of next generation distributed heterogeneous software systems. We define a new behavioural equivalence for Web services, based on bisimilarity and inspired by recent advances in the theory of reactive systems. The equivalence is ..."
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Cited by 7 (4 self)
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Web services are emerging as a promising technology for the development of next generation distributed heterogeneous software systems. We define a new behavioural equivalence for Web services, based on bisimilarity and inspired by recent advances in the theory of reactive systems. The equivalence is compositional and decidable, and it provides a firm ground for enhanced behaviouraware discovery and for a sound incremental development of services and service compositions.
Pictures of Processes: Automated Graph Rewriting for Monoidal Categories and Applications to Quantum Computing
, 2012
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Recognizable Graph Languages for Checking Invariants
, 2010
"... We generalize the ordertheoretic variant of the MyhillNerode theorem to graph languages, and characterize the recognizable graph languages as the class of languages for which the MyhillNerode quasi order is a well quasi order. In the second part of the paper we restrict our attention to graphs o ..."
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Cited by 6 (3 self)
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We generalize the ordertheoretic variant of the MyhillNerode theorem to graph languages, and characterize the recognizable graph languages as the class of languages for which the MyhillNerode quasi order is a well quasi order. In the second part of the paper we restrict our attention to graphs of bounded interface size, and use MyhillNerode quasi orders to verify that, for such bounded graphs, a recognizable graph property is an invariant of a graph transformation system. A recognizable graph property is a recognizable graph language, given as an automaton functor. Finally, we present an algorithm to approximate the MyhillNerode ordering.
V.: Structured cospans: an algebra of interaction protocols
 In: CALCO’07. LNCS
"... Abstract. We extend the theory of (co)spans as a means of providing an algebraic approach to complex interactions as they arise in softwareintensive systems. In order to make interconnections independent of the nature of components involved, interaction protocols are formalised not in terms of mor ..."
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Abstract. We extend the theory of (co)spans as a means of providing an algebraic approach to complex interactions as they arise in softwareintensive systems. In order to make interconnections independent of the nature of components involved, interaction protocols are formalised not in terms of morphisms (i.e. partof relationships) but a generalised notion of (co)span in which the arms are structured morphisms – the head (the glue of the protocol) and the hands (the interfaces of the protocol) belong to different categories, the category of glues being coordinated over that of the interfaces. The proposed generalization sheds some additional light into adjunctions in bicategories, namely on the factorisation of left adjoint 2sided enrichments. 1
Variable binding, symmetric monoidal closed theories, and bigraphs
 In Bravetti and Zavattaro [2
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Conditional Reactive Systems
, 2011
"... We lift the notion of nested application conditions from graph transformation systems to the general categorical setting of reactive systems as defined by Leifer and Milner. This serves two purposes: first, we enrich the formalism of reactive systems by adding application conditions for rules; secon ..."
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We lift the notion of nested application conditions from graph transformation systems to the general categorical setting of reactive systems as defined by Leifer and Milner. This serves two purposes: first, we enrich the formalism of reactive systems by adding application conditions for rules; second, it turns out that some constructions for graph transformation systems (such as computing weakest preconditions and strongest postconditions and showing local confluence by means of critical pair analysis) can be done very elegantly in the more general setting.