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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 14 (4 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 (2 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.
On the invariance of the unitary cost model for head reduction (long version). Available at http://arxiv.org/abs/1202.1641
"... The λcalculus is a widely accepted computational model of higherorder functional programs, yet there is not any direct and universally accepted cost model for it. As a consequence, the computational difficulty of reducing λterms to their normal form is typically studied by reasoning on concrete i ..."
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Cited by 6 (3 self)
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The λcalculus is a widely accepted computational model of higherorder functional programs, yet there is not any direct and universally accepted cost model for it. As a consequence, the computational difficulty of reducing λterms to their normal form is typically studied by reasoning on concrete implementation algorithms. In this paper, we show that when head reduction is the underlying dynamics, the unitary cost model is indeed invariant. This improves on known results, which only deal with weak (callbyvalue or callbyname) reduction. Invariance is proved by way of a linear calculus of explicit substitutions, which allows to nicely decompose any head reduction step in the λcalculus into more elementary substitution steps, thus making the combinatorics of headreduction easier to reason about. The technique is also a promising tool to attack what we see as the main open problem, namely understanding for which normalizing strategies the unitary cost model is invariant, if any.
A Theory of Explicit Substitutions with Safe and Full Composition
 Logical Methods in Computer Science
"... Vol. 5 (3:1) 2009, pp. 1–29 ..."
RPO, SECONDORDER CONTEXTS, AND λCALCULUS
"... Abstract. First, we extend LeiferMilner RPO theory, by giving general conditions to obtain IPO labelled transition systems (and bisimilarities) with a reduced set of transitions, and possibly finitely branching. Moreover, we study the weak variant of LeiferMilner theory, by giving general conditio ..."
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Abstract. First, we extend LeiferMilner RPO theory, by giving general conditions to obtain IPO labelled transition systems (and bisimilarities) with a reduced set of transitions, and possibly finitely branching. Moreover, we study the weak variant of LeiferMilner theory, by giving general conditions under which the weak bisimilarity is a congruence. Then, we apply such extended RPO technique to the lambdacalculus, endowed with lazy and call by value reduction strategies. We show that, contrary to process calculi, one can deal directly with the lambdacalculus syntax and apply LeiferMilner technique to a category of contexts, provided that we work in the framework of weak bisimilarities. However, even in the case of the transition system with minimal contexts, the resulting bisimilarity is infinitely branching, due to the fact that, in standard context categories, parametric rules such as the betarule can be represented only by infinitely many ground rules. To overcome this problem, we introduce the general notion of secondorder context
Computation in the Informatic Jungle
, 2010
"... Informatics bridges Turingcomputation and interactive behaviour; examples of the latter include ubiquitous/pervasive and biological systems. But how does a model of computation fit within a model of less disciplined informatic behaviour? This paper offers a precise treatment of that relationship, i ..."
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Informatics bridges Turingcomputation and interactive behaviour; examples of the latter include ubiquitous/pervasive and biological systems. But how does a model of computation fit within a model of less disciplined informatic behaviour? This paper offers a precise treatment of that relationship, identifying a class of calculational bigraphical reactive systems. We show how such a system contain a confluent calculation submodel, and how calculation only ever enables, never prevents, informatic behaviour of the larger model. We submit these results as a modest but essential beginning of a unified informatic theory.
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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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.
Type Systems for Bigraphs
"... We propose a novel and uniform approach to type systems for (process) calculi, which roughly pushes the challenge of designing type systems and proving properties about them to the metamodel of bigraphs. Concretely, we propose to define type systems for the term language for bigraphs, which is base ..."
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We propose a novel and uniform approach to type systems for (process) calculi, which roughly pushes the challenge of designing type systems and proving properties about them to the metamodel of bigraphs. Concretely, we propose to define type systems for the term language for bigraphs, which is based on a fixed set of elementary bigraphs and operators on these. An essential elementary bigraph is an ion, to which a control can be attached modelling its kind (its ordered number of channels and whether it is a guard), e.g. an input prefix of πcalculus. A model of a calculus is then a set of controls and a set of reaction rules, collectively a bigraphical reactive system (BRS). Possible advantages of developing bigraphical type systems include: a deeper understanding of a type system itself and its properties; transfer of the type systems to the concrete family of calculi that the BRS models; and the possibility of modularly adapting the type systems to extensions of the BRS (with new controls). As proof of concept we present a model of a πcalculus, develop an i/otype system with subtyping on this model, prove crucial properties (including subject reduction) for this type system, and transfer these properties to the (typed) πcalculus.