Deriving Bisimulation Congruences for Reactive Systems

Leifer, James J.; Milner, Robin

doi:10.1007/3-540-44618-4_19

Cited by 137 publications

(207 citation statements)

References 21 publications

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“…However, there are fundamental problems, mainly caused by graphs having non-trivial automorphisms (see, e.g., the counterexample in [13] on pages 80/81, which can be directly transferred into our framework). We believe, however, that our construction is very close in spirit to the notion of relative pushouts introduced by Leifer and Milner and that it should be possible to show the equivalence of these two notions in a suitable graph category with support.…”

Section: Resultsmentioning

confidence: 99%

“…So the idea which was formulated in the papers of Leifer/Milner [13,14], Sewell [24] and Sassone/Sobocinski [23] is to automatically derive a labelled…”

Section: Introductionmentioning

confidence: 99%

“…Using all possible contexts as labels would also result in a bisimulation congruence, but we do not gain anything compared to quantification over all contexts. In [13,14] the notion of "minimal context" is formalized as the categorical concept of relative pushout respectively idem pushout. This notion has also been applied to bigraphs [10].…”

Section: Introductionmentioning

confidence: 99%

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Deriving Bisimulation Congruences in the DPO Approach to Graph Rewriting

Ehrig

König

2004

Lecture Notes in Computer Science

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Abstract. Motivated by recent work on the derivation of labelled transitions and bisimulation congruences from unlabelled reaction rules, we show how to solve this problem in the DPO (double-pushout) approach to graph rewriting. Unlike in previous approaches, we consider graphs as objects, instead of arrows, of the category under consideration. This allows us to present a very simple way of deriving labelled transitions (called rewriting steps with borrowed context) which smoothly integrates with the DPO approach, has a very constructive nature and requires only a minimum of category theory. The core part of this paper is the proof sketch that the bisimilarity based on rewriting with borrowed contexts is a congruence relation.

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Section: Resultsmentioning

confidence: 99%

“…So the idea which was formulated in the papers of Leifer/Milner [13,14], Sewell [24] and Sassone/Sobocinski [23] is to automatically derive a labelled…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Deriving Bisimulation Congruences in the DPO Approach to Graph Rewriting

Ehrig

König

2004

Lecture Notes in Computer Science

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“…The question as to whether or not term a in context c manifests a redex l becomes now whether there exists a suitable context d such that ca = dl. This allows us to express the minimality of c by ranging over all equations of the kind c a = d l, seeking for unique ways to factor c through c. In §2 we recall how such universal property is elegantly expressed by the notion of idem-relative-pushout, a breakthrough due Leifer and Milner [4]. Remarkably, such formalisation supports the central 'congruence theorem' that bisimulation on the labelled transition systems derived following the theory is a congruence, i.e., it is closed under all contexts.…”

Section: A An a B A(n) B A | B A | Bmentioning

confidence: 99%

“…Indeed, there is no unique mediation between the squares in the slice of 1: By an idem-relative-pushout [4] we mean the (square) diagram in C obtained by applying the forgetful functor U W : C/W → C (which projects V, r to V) to a pushout diagram in C/W. Let I denote the class of IPOs in C.…”

Section: Lemma 2 Pap Has Slice Pushoutsmentioning

confidence: 99%

Labels from Reductions: Towards a General Theory

Klin

Sassone

Sobociński

2005

Algebra and Coalgebra in Computer Science

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Deriving Weak Bisimulation Congruences from Reduction Systems

Bruni

Gadducci

Montanari

et al. 2005

Lecture Notes in Computer Science

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The focus of process calculi is interaction rather than computation, and for this very reason: (i) their operational semantics is conveniently expressed by labelled transition systems (LTSs) whose labels model the possible interactions of a process with the environment; (ii) their abstract semantics is conveniently expressed by observational congruences. However, many current-day process calculi are more easily equipped with reduction semantics, where the notion of observable action is missing. Recent techniques attempted to bridge this gap by synthesising LTSs whose labels are process contexts that enable reactions and for which bisimulation is a congruence. Starting from Sewell's set-theoretic construction, category-theoretic techniques were defined and based on Leifer and Milner's relative pushouts, later refined by Sassone and the fourth author to deal with structural congruences given as groupoidal 2-categories. Building on recent works concerning observational equivalences for tile logic, the paper demonstrates that double categories provide an elegant setting in which the aforementioned contributions can be studied. Moreover, the formalism allows for a straightforward and natural definition of weak observational congruence

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Deriving Bisimulation Congruences for Reactive Systems

Cited by 137 publications

References 21 publications

Deriving Bisimulation Congruences in the DPO Approach to Graph Rewriting

Deriving Bisimulation Congruences in the DPO Approach to Graph Rewriting

Labels from Reductions: Towards a General Theory

Deriving Weak Bisimulation Congruences from Reduction Systems

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