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Reactive Systems over Cospans
, 2005
"... The theory of reactive systems, introduced by Leifer and Milner and previously extended by the authors, allows the derivation of wellbehaved labelled transition systems (LTS) for semantic models with an underlying reduction semantics. The derivation procedure requires the presence of certain colimi ..."
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Cited by 47 (3 self)
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The theory of reactive systems, introduced by Leifer and Milner and previously extended by the authors, allows the derivation of wellbehaved labelled transition systems (LTS) for semantic models with an underlying reduction semantics. The derivation procedure requires the presence of certain colimits (or, more usually and generally, bicolimits) which need to be constructed separately within each model. In this paper, we o#er a general construction of such bicolimits in a class of bicategories of cospans. The construction sheds light on as well as extends Ehrig and Konig's rewriting via borrowed contexts and opens the way to a unified treatment of several applications.
Saturated semantics for reactive systems
 LOGIC IN COMPUTER SCIENCE
, 2006
"... The semantics of process calculi has traditionally been specified by labelled transition systems (LTS), 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 (b ..."
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Cited by 36 (18 self)
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The semantics of process calculi has traditionally been specified by labelled transition systems (LTS), 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 intended 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 a subset of the open πcalculus. Indeed, we prove that our equivalences are congruences and that they coincide with logical equivalence and open bisimilarity respectively, while equivalences studied in previous works are strictly finer.
A congruence for Petri Nets
 PNGT’04
, 2004
"... We introduce a way of viewing Petri nets as open systems. This is done by considering a bicategory of cospans over a category of p/t nets and embeddings. We derive a labelled transition system (LTS) semantics for such nets using GIPOs and characterise the resulting congruence. Technically, our resul ..."
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Cited by 24 (10 self)
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We introduce a way of viewing Petri nets as open systems. This is done by considering a bicategory of cospans over a category of p/t nets and embeddings. We derive a labelled transition system (LTS) semantics for such nets using GIPOs and characterise the resulting congruence. Technically, our results are similar to the recent work by Milner on applying the theory of bigraphs to Petri Nets. The two main differences are that we treat p/t nets instead of c/e nets and we deal directly with a category of nets instead of encoding them into bigraphs.
Adhesive HighLevel Replacement Systems: A New Categorical Framework for Graph Transformation
, 2006
"... Adhesive highlevel replacement (HLR) systems are introduced as a new categorical framework for graph transformation in the double pushout (DPO) approach, which combines the wellknown concept of HLR systems with the new concept of adhesive categories introduced by Lack and Sobociński. In this pa ..."
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Cited by 21 (12 self)
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Adhesive highlevel replacement (HLR) systems are introduced as a new categorical framework for graph transformation in the double pushout (DPO) approach, which combines the wellknown concept of HLR systems with the new concept of adhesive categories introduced by Lack and Sobociński. In this paper we show that most of the HLR properties, which had been introduced to generalize some basic results from the category of graphs to highlevel structures, are valid already in adhesive HLR categories. This leads to a smooth categorical theory of HLR systems which can be applied to a large variety of graphs and other visual models. As a main new result in a categorical framework we show the Critical Pair Lemma for the local confluence of transformations. Moreover we present a new version of embeddings and extensions for transformations in our framework of adhesive HLR systems.
Labels from Reductions: Towards a General Theory
 In Algebra and Coalgebra in Computer Science, Calco ’05, volume 3629 of LNCS
, 2005
"... Abstract. We consider open terms and parametric rules in the context of the systematic derivation of labelled transitions from reduction systems. ..."
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Cited by 16 (3 self)
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Abstract. We consider open terms and parametric rules in the context of the systematic derivation of labelled transitions from reduction systems.
A coalgebraic theory of reactive systems
, 1999
"... In this report we study the connection between two well known models for interactive systems. Reactive Systems à la Leifer and Milner allow to derive an interactive semantics from a reduction semantics guaranteeing, semantics (bisimilarity). Universal Coalgebra provides a categorical framework where ..."
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Cited by 9 (1 self)
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In this report we study the connection between two well known models for interactive systems. Reactive Systems à la Leifer and Milner allow to derive an interactive semantics from a reduction semantics guaranteeing, semantics (bisimilarity). Universal Coalgebra provides a categorical framework where bisimilarity can be characterized as final semantics, i.e., as the unique morphism to the final coalgebra. Moreover, if lifting a coalgebra to a structured setting is possible, then bisimilarity is compositional with respect to the lifted structure. Here we show that for every reactive 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.
Pictures of Processes: Automated Graph Rewriting for Monoidal Categories and Applications to Quantum Computing
, 2012
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Towards Algebraic HighLevel Systems as Weak Adhesive HLR Categories
"... Adhesive highlevel replacement (HLR) systems have been recently established as a suitable categorical framework for double pushout transformations based on weak adhesive HLR categories. Among different types of graphs and graphlike structures, various kinds of Petri nets and algebraic highlevel ( ..."
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Cited by 6 (0 self)
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Adhesive highlevel replacement (HLR) systems have been recently established as a suitable categorical framework for double pushout transformations based on weak adhesive HLR categories. Among different types of graphs and graphlike structures, various kinds of Petri nets and algebraic highlevel (AHL) nets are interesting instantiations of adhesive HLR systems. AHL nets combine algebraic specifications with Petri nets to allow the modeling of data, data flow and data changes within the net. For the development and analysis of reconfigurable systems, not only AHL schemas based on an algebraic specification and AHL nets using an additional algebra should be considered, but also AHL systems which additionally include markings of nets. In this paper, we summarize the results for different kinds of AHL schemas and nets, and extend these results
Coalgebraic Models for Reactive Systems ⋆
"... Abstract. Reactive Systems à la Leifer and Milner allow to derive from a reaction semantics definition an LTS equipped with a bisimilarity relation which is a congruence. This theory has been extended by the authors (together with Barbara König) in order to handle saturated bisimilarity, a coarser e ..."
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Abstract. Reactive Systems à la Leifer and Milner allow to derive from a reaction semantics definition an LTS equipped with a bisimilarity relation which is a congruence. This theory has been extended by the authors (together with Barbara König) in order to handle saturated bisimilarity, a coarser equivalence that is more adequate for some interesting formalisms, such as logic programming and open picalculus. In this paper we recast the theory of Reactive Systems inside Universal Coalgebra. This construction is particularly useful for saturated bisimilarity, which can be seen as final semantics of Normalized Coalgebras. These are structured coalgebras (not bialgebras) where the sets of transitions are minimized rather than maximized as in saturated LTS, still yielding the same semantics. We give evidence the effectiveness of our approach minimizing an Open Petri net in
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"... Sémantique operationelle et dénotationelle du picalcul réversible Operational and denotational semantics for the reversible picalculus soutenue par ..."
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Sémantique operationelle et dénotationelle du picalcul réversible Operational and denotational semantics for the reversible picalculus soutenue par