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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.
Locating Reaction with 2categories
, 2004
"... Groupoidal relative pushouts (GRPOs) have recently been proposed by the authors as a new foundation for Leifer and Milner's approach to deriving labelled bisimulation congruences from reduction systems. In this paper, we develop the theory of GRPOs further, proving that wellknown equivalences, othe ..."
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Cited by 11 (1 self)
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Groupoidal relative pushouts (GRPOs) have recently been proposed by the authors as a new foundation for Leifer and Milner's approach to deriving labelled bisimulation congruences from reduction systems. In this paper, we develop the theory of GRPOs further, proving that wellknown equivalences, other than bisimulation, are congruences. To demonstrate the type of category theoretic arguments which are inherent in the 2categorical approach, we construct GRPOs in a category of `bunches and wirings.' Finally, we prove that the 2categorical theory of GRPOs is a generalisation of the approaches based on Milner's precategories and Leifer's functorial reactive systems.
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.
Synthesising Labelled Transitions and Operational Congruences in Reactive Systems, Part 1
 IN INT
, 2002
"... The dynamics of process calculi, e.g. CCS, have often been defined using a labelled transition system (LTS). More recently it has become common when defining dynamics to use reaction rules i.e. unlabelled transition rules together with a structural congruence. This form, which I call a reactiv ..."
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Cited by 6 (1 self)
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The dynamics of process calculi, e.g. CCS, have often been defined using a labelled transition system (LTS). More recently it has become common when defining dynamics to use reaction rules i.e. unlabelled transition rules together with a structural congruence. This form, which I call a reactive system, is highly expressive but is limited in an important way: LTSs lead more naturally to operational equivalences and preorders. This paper shows how to synthesise an LTS for a wide range of reactive systems. A label for an agent (process) `a' is defined to be any context `F' which intuitively is just large enough so that the agent `Fa' (`a' in context `F') is able to perform a reaction step. The key contribution of my work is the precise definition of "just large enough" in terms of the categorical notion of relative pushout (RPO). I then prove that several operational equivalences and preorders (strong bisimulation, weak bisimulation, the traces preorder, and the failures preorder) are congruences when sufficient RPOs exist.
Congruences for Contextual GraphRewriting
, 2004
"... We introduce a comprehensive operational semantic theory of graphrewriting. Graphrewriting here is ..."
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We introduce a comprehensive operational semantic theory of graphrewriting. Graphrewriting here is
Model checking for nominal calculi
 IN FOSSACS, VOLUME 3441 OF LNCS
, 2005
"... Nominal calculi have been shown very effective to formally model a variety of computational phenomena. The models of nominal calculi have often infinite states, thus making model checking a difficult task. In this note we survey some of the approaches for model checking nominal calculi. Then, we f ..."
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Cited by 6 (2 self)
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Nominal calculi have been shown very effective to formally model a variety of computational phenomena. The models of nominal calculi have often infinite states, thus making model checking a difficult task. In this note we survey some of the approaches for model checking nominal calculi. Then, we focus on HistoryDependent automata, a syntaxfree automatonbased model of mobility. HistoryDependent automata have provided the formal basis to design and implement some existing verification toolkits. We then introduce a novel syntaxfree setting to model the symbolic semantics of a nominal calculus. Our approach relies on the notions of reactive systems and observed borrowed contexts introduced by Leifer and Milner, and further developed by Sassone, Lack and Sobocinski. We argue that the symbolic semantics model based on borrowed contexts can be conveniently applied to web service discovery and binding.
Coinductive Reasoning for Contextual GraphRewriting
, 2004
"... We introduce a comprehensive semantic theory of graph rewriting. The theory is operational, and therefore, lends itself to the application of coinductive principles. The central idea is recasting rewriting frameworks as reactive systems with the resulting contextual equivalences. Specifically, a gra ..."
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Cited by 3 (1 self)
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We introduce a comprehensive semantic theory of graph rewriting. The theory is operational, and therefore, lends itself to the application of coinductive principles. The central idea is recasting rewriting frameworks as reactive systems with the resulting contextual equivalences. Specifically, a graph rewriting system is associated with a labelled transition system, so that the corresponding bisimulation is a congruence with respect to arbitrary graph contexts.
Structural congruences and structural operational semantics
, 2004
"... Structural congruences have been used to define the semantics and to capture inherent properties of language constructs. They have been used as an addendum to transition system specifications in Plotkin’s style of Structural Operational Semantics (SOS). However, there has been little theoretical wor ..."
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Cited by 1 (1 self)
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Structural congruences have been used to define the semantics and to capture inherent properties of language constructs. They have been used as an addendum to transition system specifications in Plotkin’s style of Structural Operational Semantics (SOS). However, there has been little theoretical work on establishing a formal link between theses two semantic specification frameworks. In this paper, we try to fill this gap by accommodating structural congruences inside transition system specifications. The Contributions of this paper can be summarized as follows: 1. Three interpretations of structural congruences in the SOS framework are presented; 2. The three interpretations are compared formally; 3. Syntactic criteria of a congruence format for structural congruences are given and proved correct; 4. Welldefinedness criteria for transition system specifications with negative premises are extended to the setting with structural congruences; 5. Operational and equational conservative extensions of languages with structural congruences are studied.
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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Cited by 1 (0 self)
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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