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Process Bisimulation via a Graphical Encoding
 IN: ICGT ‘06. VOLUME 4178 OF LNCS
, 2006
"... The paper presents a case study on the synthesis of labelled transition systems (ltss) for process calculi, choosing as testbed Milner’s Calculus of Communicating System (ccs). The proposal is based on a graphical encoding: each ccs process is mapped into a graph equipped with suitable interfaces, s ..."
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The paper presents a case study on the synthesis of labelled transition systems (ltss) for process calculi, choosing as testbed Milner’s Calculus of Communicating System (ccs). The proposal is based on a graphical encoding: each ccs process is mapped into a graph equipped with suitable interfaces, such that the denotation is fully abstract with respect to the usual structural congruence. Graphs with interfaces are amenable to the synthesis mechanism based on borrowed contexts (bcs), proposed by Ehrig and König (which are an instance of relative pushouts, originally introduced by Milner and Leifer). The bc mechanism allows the effective construction of an lts that has graphs with interfaces as both states and labels, and such that the associated bisimilarity is automatically a congruence. Our paper focuses on the analysis of the lts distilled by exploiting the encoding of ccs processes: besides offering some technical contributions towards the simplification of the bc mechanism, the key result of our work is the proof that the bisimilarity on processes obtained via bcs coincides with the standard strong bisimilarity for ccs.
A First Study of Compositionality in Graph Transformation
"... Abstract. Graph transformation works under a wholeworld assumption. In modelling realistic systems, this typically makes for large graphs and sometimes also large, hard to understand rules. From process algebra, on the other hand, we know the principle of reactivity, meaning that the system being m ..."
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Abstract. Graph transformation works under a wholeworld assumption. In modelling realistic systems, this typically makes for large graphs and sometimes also large, hard to understand rules. From process algebra, on the other hand, we know the principle of reactivity, meaning that the system being modelled is embedded in an environment with which it continually interacts. This has the advantage of allowing modular system specifications and correspondingly smaller descriptions of individual components. Reactivity can alternatively be understood as enabling compositionality: the specification of components and subsystems are composed to obtain the complete model. In this work we show a way to ingest graph transformation with compositionality, reaping the same benefits from modularity as enjoyed by process algebra. In particular, using the existing concept of graph interface, we show under what circumstances rules can be decomposed into smaller subrules, each working on a subgraph of the complete, wholeworld graph, in such a way that the effect of the original rule is precisely captured by the synchronisation of subrules. 1
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.
Deriving Bisimulation Congruences with Borrowed Contexts (Abstract)
, 2007
"... In the last few years the problem of deriving labelled transitions and bisimulation congruences from unlabelled reaction or rewriting rules has received great attention. This line of research was motivated by the theory of bisimulation congruences for process calculi, such as the πcalculus [19, 14] ..."
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In the last few years the problem of deriving labelled transitions and bisimulation congruences from unlabelled reaction or rewriting rules has received great attention. This line of research was motivated by the theory of bisimulation congruences for process calculi, such as the πcalculus [19, 14]. A bisimilarity defined on unlabelled reduction rules is usually not a congruence, that is, it is not closed under the operators of the process calculus. Congruence is a desirable property since it allows one to replace a subsystem with an equivalent one without changing the behaviour of the overall system and futhermore helps to make bisimilarity proofs modular. Previous solutions have been to either require that two processes are related if and only if they are bisimilar under all possible contexts [15] or to derive a labelled transition system manually. Since the first solution needs quantification over all possible contexts, proofs of bisimilarity can be very complicated. In the second solution, proofs tend to be much easier, but it is necessary to show that the labelled variant of the transition system is equivalent to the unlabelled
www.elsevier.com/locate/entcs GReactive Systems as Coalgebras
"... 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 definitions employing reduction semantics are sometimes more natural. Reactive Systems à la Leifer and Milner allow to derive from a re ..."
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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 definitions employing reduction semantics are sometimes more natural. Reactive Systems à la Leifer and Milner allow to derive from a reduction semantics definition an LTS equipped with a bisimilarity relation which is a congruence. This theory has been extended to GReactive Systems by Sassone and Sobocinki in order to properly handle structural equivalence. Universal Coalgebra provides a categorical framework where bisimilarity can be characterized as final semantics, i.e., each LTS can be mapped to a minimal realization identifying bisimilar states. Moreover, it is often possible to lift coalgebras to an algebraic setting (yielding bialgebras by Turi and Plotkin or, slightly more generally, structured coalgebras by Corradini, Heckel and Montanari) with the property that bisimilarity is compositional with respect to the lifted structure. The existence of minimal realizations is of theoretical interest, but it is even more of practical interest whenever LTSs are employed for finite state verification. In this paper we show that for every GReactive System we can build a coalgebra. Furthermore, if bisimilarity is compositional in the Reactive System, then we can lift this coalgebra to a structured coalgebra. Keywords: coalgebra Process calculus, labelled transition system, reactive systems, Greactve systems, universal 1
Parallel and Sequential Independence for Borrowed Contexts
, 2008
"... Parallel and sequential independence are central concepts in the concurrency theory of the double pushout (dpo) approach to graph rewriting. However, so far those same notions were missing for dpo rewriting extended with borrowed contexts (dpobc), a formalism used for equipping dpo derivations with ..."
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Parallel and sequential independence are central concepts in the concurrency theory of the double pushout (dpo) approach to graph rewriting. However, so far those same notions were missing for dpo rewriting extended with borrowed contexts (dpobc), a formalism used for equipping dpo derivations with labels and introduced for modeling open systems that interact with the environment. In this work we propose the definition of parallel and sequential independence for dpobc rewriting, and we prove that these novel notions allow generalizing the ChurchRosser and parallelism theorems holding for dpo rewriting. Most importantly, we show that the dpobc version of these theorems still guarantees the local confluence and the parallel execution of pairs of independent dpobc derivations.
GReactive Systems as Coalgebras
"... 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 definitions employing reduction semantics are sometimes more natural. Reactive Systems à la Leifer and Milner allow to derive from a re ..."
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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 definitions employing reduction semantics are sometimes more natural. Reactive Systems à la Leifer and Milner allow to derive from a reduction semantics definition an LTS equipped with a bisimilarity relation which is a congruence. This theory has been extended to GReactive Systems by Sassone and Sobocinki in order to properly handle structural equivalence. Universal Coalgebra provides a categorical framework where bisimilarity can be characterized as final semantics, i.e., each LTS can be mapped to a minimal realization identifying bisimilar states. Moreover, it is often possible to lift coalgebras to an algebraic setting (yielding bialgebras by Turi and Plotkin or, slightly more generally, structured coalgebras by Corradini, Heckel and Montanari) with the property that bisimilarity is compositional with respect to the lifted structure. The existence of minimal realizations is of theoretical interest, but it is even more of practical interest whenever LTSs are employed for finite state verification. In this paper we show that for every GReactive System we can build a coalgebra. Furthermore, if bisimilarity is compositional in the Reactive System, then we can lift this coalgebra to a structured coalgebra. 1
Viewbased Modelling and StateSpace Generation for Graph Transformation Systems
"... Abstract: Modelling complex systems by graph transformation, we face scalability challenges both in our ability to create and understand these models and in the ability of tools to analyse them. To address these problems we propose to model graph transformation systems in views which can be underst ..."
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Abstract: Modelling complex systems by graph transformation, we face scalability challenges both in our ability to create and understand these models and in the ability of tools to analyse them. To address these problems we propose to model graph transformation systems in views which can be understood and analysed separately. In particular, we show that transition systems can be generated separately for different views which, when synchronised using a CSPlike operator, yield a system that is bisimilar to the original global system.