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18
Matching of Bigraphs
 PREPRINT OF GTVC 2006
, 2006
"... We analyze the matching problem for bigraphs. In particular, we present a sound and complete inductive characterization of matching of binding bigraphs. Our results pave the way for a provably correct matching algorithm, as needed for an implementation of bigraphical reactive systems. ..."
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Cited by 20 (11 self)
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We analyze the matching problem for bigraphs. In particular, we present a sound and complete inductive characterization of matching of binding bigraphs. Our results pave the way for a provably correct matching algorithm, as needed for an implementation of bigraphical reactive systems.
Reactive Systems, Barbed Semantics, and the Mobile Ambients
"... Reactive systems, proposed by Leifer and Milner, represent a metaframework aimed at deriving behavioral congruences for those specification formalisms whose operational semantics is provided by rewriting rules. Despite its applicability, reactive systems suffered so far from two main drawbacks. Fir ..."
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Cited by 17 (6 self)
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Reactive systems, proposed by Leifer and Milner, represent a metaframework aimed at deriving behavioral congruences for those specification formalisms whose operational semantics is provided by rewriting rules. Despite its applicability, reactive systems suffered so far from two main drawbacks. First of all, no technique was found for recovering a set of inference rules, e.g. in the socalled SOS style, for describing the distilled observational semantics. Most importantly, the efforts focussed on strong bisimilarity, tackling neither weak nor barbed semantics. Our paper addresses both issues, instantiating them on a calculus whose semantics is still in a flux: Cardelli and Gordon’s mobile ambients. While the solution to the first issue is tailored over our case study, we provide a general framework for recasting (weak) barbed equivalence in the reactive systems formalism. Moreover, we prove that our proposal captures the behavioural semantics for mobile ambients proposed by Rathke and Sobociński and by Merro and Zappa Nardelli.
Abstract Semantics by Observable Contexts
, 2008
"... The operational behavior of interactive systems is usually given in terms of transition systems labeled with actions, which, when visible, represent both observations and interactions with the external world. The abstract semantics is given in terms of behavioral equivalences, which depend on the ac ..."
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Cited by 9 (3 self)
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The operational behavior of interactive systems is usually given in terms of transition systems labeled with actions, which, when visible, represent both observations and interactions with the external world. The abstract semantics is given in terms of behavioral equivalences, which depend on the action labels and on the amount of branching structure considered. Behavioural equivalences are often congruences with respect to the operations of the language, and this property expresses the compositionality of the abstract semantics. A simpler approach, inspired by classical formalisms like λcalculus, Petri nets, term and graph rewriting, and pioneered by the Chemical Abstract Machine [1], defines operational semantics by means of structural axioms and reaction rules. Process calculi representing complex systems, in particular those able to generate and communicate names, are often defined in this way, since structural axioms give a clear idea of the intended structure of the states while reaction rules, which are often nonconditional, give a direct account of the possible steps. Transitions caused by reaction rules, however, are not labeled, since
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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Cited by 8 (4 self)
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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.
Composition and decomposition of DPO transformations with borrowed contexts
, 2006
"... Doublepushout (DPO) transformations with borrowed context extend the standard DPO approach by allowing part of the graph needed in a transformation to be borrowed from the environment. The bisimilarity based on the observation of borrowed contexts is a congruence, thus facilitating system analysis ..."
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Cited by 8 (3 self)
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Doublepushout (DPO) transformations with borrowed context extend the standard DPO approach by allowing part of the graph needed in a transformation to be borrowed from the environment. The bisimilarity based on the observation of borrowed contexts is a congruence, thus facilitating system analysis. In this paper, focusing on the situation in which the states of a global system are built out of local components, we show that DPO transformations with borrowed context defined on a global system state can be decomposed into corresponding transformations on the local states and vice versa. Such composition and decomposition theorems, developed in the framework of adhesive categories, can be seen as a first step towards an inductive definition, in sos style, of the labelled transition system associated to a graph transformation system. As a special case we show how an ordinary DPO transformation on a global system state can be decomposed into local DPO transformations with borrowed context using the same production.
Symbolic semantics revisited
, 2008
"... Symbolic bisimulations were introduced as a mean to define valuepassing process calculi using smaller, possibly finite labelled transition systems, equipped with symbolic actions. Similar ideas have been used for modeling with fewer transitions the input behavior of open and asynchronous πcalculu ..."
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Cited by 8 (4 self)
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Symbolic bisimulations were introduced as a mean to define valuepassing process calculi using smaller, possibly finite labelled transition systems, equipped with symbolic actions. Similar ideas have been used for modeling with fewer transitions the input behavior of open and asynchronous πcalculus. In this paper we generalize the symbolic technique and apply the resulting theory to these two cases, rederiving existing results. We also apply our approach to a new setting, i.e. open Petri nets, with the usual result of reducing input transitions. Our theory generalizes Leifer and Milner reactive systems by adding observations.
A Decentralized Implementation Of Mobile Ambients
, 2008
"... We present a graphical implementation for finite processes of the mobile ambients calculus. Our encoding uses unstructured (i.e., non hierarchical) graphs and it is sound and complete with respect to the structural congruence of the calculus (that is, two processes are equivalent iff they are mapp ..."
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Cited by 4 (4 self)
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We present a graphical implementation for finite processes of the mobile ambients calculus. Our encoding uses unstructured (i.e., non hierarchical) graphs and it is sound and complete with respect to the structural congruence of the calculus (that is, two processes are equivalent iff they are mapped into isomorphic graphs). With respect to alternative proposals for the graphical implementation of mobile ambients, our encoding distinguishes the syntactic structure of a process from the activation order of a process components. Our solution faithfully captures a basic feature of the calculus (ambients can be nested and reductions are propagated across ambient nesting) and it allows to model the reduction semantics via a graph transformation system containing just three rules.
Reactive Systems, (Semi)Saturated Semantics and Coalgebras on Presheaves
, 2009
"... The semantics of process calculi has traditionally been specified by labelled transition systems (ltss), but with the development of name calculi it turned out that reaction rules (i.e., unlabelled transition rules) are often more natural. This leads to the question of how behavioural equivalences ( ..."
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Cited by 1 (0 self)
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The semantics of process calculi has traditionally been specified by labelled transition systems (ltss), but with the development of name calculi it turned out that reaction rules (i.e., unlabelled transition rules) are often more natural. This leads to the question of how behavioural equivalences (bisimilarity, trace equivalence, etc.) defined for lts can be transferred to unlabelled transition systems. Recently, in order to answer this question, several proposals have been made with the aim of automatically deriving an lts from reaction rules in such a way that the resulting equivalences are congruences. Furthermore these equivalences should agree with the standard semantics, whenever one exists. In this paper we propose saturated semantics, based on a weaker notion of observation and orthogonal to all the previous proposals, and we demonstrate the appropriateness of our semantics by means of two examples: logic programming and open Petri nets. We also show that saturated semantics can be efficiently characterized through the so called semisaturated games. Finally, we provide coalgebraic models relying on presheaves.
Bisimulation Verification for the DPO Approach with Borrowed Contexts
 ECEASST
, 2007
"... Bisimilarity is the most widespread notion of behavioral equivalence and hence algorithms for bisimulation checking are of fundamental importance for verifying that two systems are behaviorally equivalent (seen from the perspective of the environment). We investigate this problem in the context of b ..."
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Cited by 1 (1 self)
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Bisimilarity is the most widespread notion of behavioral equivalence and hence algorithms for bisimulation checking are of fundamental importance for verifying that two systems are behaviorally equivalent (seen from the perspective of the environment). We investigate this problem in the context of behavioral equivalences of graphs and graph transformation systems, where the extension of the DPO approach to borrowed contexts provides us with a formal basis for reasoning about bisimilarity of graphs. In this paper we extend Hirschkoff’s onthefly algorithm for bisimulation checking, enabling it to verify whether two graphs are bisimilar with respect to a given set of productions. We then apply this framework to refactoring problems and verify instances of a model transformation which describes the minimization of deterministic finite automata.