## Process Bisimulation via a Graphical Encoding (2006)

Venue: | IN: ICGT ‘06. VOLUME 4178 OF LNCS |

Citations: | 17 - 11 self |

### BibTeX

@INPROCEEDINGS{Bonchi06processbisimulation,

author = {Filippo Bonchi and Fabio Gadducci and Barbara König},

title = {Process Bisimulation via a Graphical Encoding},

booktitle = {IN: ICGT ‘06. VOLUME 4178 OF LNCS},

year = {2006},

pages = {168--183},

publisher = {Springer}

}

### Years of Citing Articles

### OpenURL

### Abstract

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.

### Citations

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(Show Context)
Citation Context ...design and verification. The extended version of the paper [5] contains additional examples, categorical notations and detailed proofs. 2 Two Operational Semantics for CCS This section introduces ccs =-=[16]-=- and two alternative operational semantics: the classical lts semantics and the reduction semantics. Definition 1 (processes). Let N be a set of names, ranged over by a,b,c,...; τ ∈ N an invisible na... |

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Citation Context ...usly defined rs. Indeed, after Milner’s proposal of an alternative semantics for the π-calculus [17] based on reactive rules modulo a structural congruence on processes, inspired by the cham paradigm =-=[4]-=-, an ongoing stream of research has been investigating the relationship between the lts semantics for process calculi and their more abstract rs semantics. Early attempts by Sewell [22] devised a stra... |

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Citation Context ... straightforward, though, to identify the right “label” that should be distilled, starting from a previously defined rs. Indeed, after Milner’s proposal of an alternative semantics for the π-calculus =-=[17]-=- based on reactive rules modulo a structural congruence on processes, inspired by the cham paradigm [4], an ongoing stream of research has been investigating the relationship between the lts semantics... |

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Citation Context ...ore abstract rs semantics. Early attempts by Sewell [22] devised a strategy for obtaining an lts from an rs by adding contexts as labels on transitions. The technique was refined by Leifer and Milner =-=[15]-=- who introduced relative pushouts (rpos) in order to capture the notion of minimal context activating a reduction. The generality of this proposal (and its bicategorical formulation due to Sassone and... |

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Citation Context ...unctions. An (hyper-)graph morphism is a pair of functions 〈fV ,fE〉 preserving the source and target functions. The corresponding category is denoted by Graph. However, we often consider typed graphs =-=[7]-=-, i.e., graphs labelled over a structure that is itself a graph. Definition 6 (typed graphs). Let T be a graph. A typed graph G over T is a graph |G|, together with a graph morphism tG : |G| →T .Amorp... |

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Citation Context ...e cham paradigm [4], an ongoing stream of research has been investigating the relationship between the lts semantics for process calculi and their more abstract rs semantics. Early attempts by Sewell =-=[22]-=- devised a strategy for obtaining an lts from an rs by adding contexts as labels on transitions. The technique was refined by Leifer and Milner [15] who introduced relative pushouts (rpos) in order to... |

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Citation Context ...alculi ensures that the synthesis of an lts can be performed, and that a compositional observational equivalence is obtained. The key technical point is the use of the borrowed context (bc) technique =-=[8]-=- as a tool to equip graph transformation in the dpo style with an lts semantics. Graphs with interfaces are amenable to the synthesis mechanism based on bcs (which are in turn an instance of rpos): th... |

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Citation Context ...relying either on standard (ground) term rewriting [15], or on extremely simplified variants of process calculi [20]:170 F. Bonchi, F. Gadducci, and B. König more elaborated proposals using bigraphs =-=[18,14]-=- result in infinitely branching ltss, banning recursive processes or failing to capture standard bisimilarity. Summing up, the aim of our work is straightforward: to present a fully-fledged case study... |

51 | Pure bigraphs: Structure and dynamics
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Citation Context ...relying either on standard (ground) term rewriting [15], or on extremely simplified variants of process calculi [20]:170 F. Bonchi, F. Gadducci, and B. König more elaborated proposals using bigraphs =-=[18,14]-=- result in infinitely branching ltss, banning recursive processes or failing to capture standard bisimilarity. Summing up, the aim of our work is straightforward: to present a fully-fledged case study... |

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Citation Context ...y.172 F. Bonchi, F. Gadducci, and B. König 3 Graphs and Their Extension with Interfaces We recall a few definitions concerning (typed hyper-)graphs, and their extension with interfaces, referring to =-=[6]-=- for a more detailed introduction. Definition 5 (graphs). A (hyper-)graph is a four-tuple 〈V,E,s,t〉 where V is the set of nodes, E is the set of edges and s, t : E → V ∗ are the source and target func... |

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Citation Context ...coded in graphs with interfaces, an instance of cospan categories [11], and process reduction is simulated by double-pushout (dpo) rewriting [1]. Since the category of cospans over graphs admits rpos =-=[21]-=-, its choice as the domain of the encoding for nominal calculi ensures that the synthesis of an lts can be performed, and that a compositional observational equivalence is obtained. The key technical ... |

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Citation Context ...sisofanlts are the graphical techniques proposed for modelling the reduction semantics of nominal calculi in [10,12]: processes are encoded in graphs with interfaces, an instance of cospan categories =-=[11]-=-, and process reduction is simulated by double-pushout (dpo) rewriting [1]. Since the category of cospans over graphs admits rpos [21], its choice as the domain of the encoding for nominal calculi ens... |

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Citation Context ...ced relative pushouts (rpos) in order to capture the notion of minimal context activating a reduction. The generality of this proposal (and its bicategorical formulation due to Sassone and Sobocinski =-=[20]-=-) allows it to be applied to a large class of formalisms. More importantly, such attempts share the basic property of synthesising a congruent bisimulation equivalence, thus ensuring that the resultin... |

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Citation Context ...n semantics of nominal calculi in [10,12]: processes are encoded in graphs with interfaces, an instance of cospan categories [11], and process reduction is simulated by double-pushout (dpo) rewriting =-=[1]-=-. Since the category of cospans over graphs admits rpos [21], its choice as the domain of the encoding for nominal calculi ensures that the synthesis of an lts can be performed, and that a composition... |

22 |
Graph rewriting for the π-calculus
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(Show Context)
Citation Context ...ckle a fully-fledged case study is the main aim of this paper. Ourstartingpointforthesynthesisofanlts are the graphical techniques proposed for modelling the reduction semantics of nominal calculi in =-=[10,12]-=-: processes are encoded in graphs with interfaces, an instance of cospan categories [11], and process reduction is simulated by double-pushout (dpo) rewriting [1]. Since the category of cospans over g... |

19 |
U.: A concurrent graph semantics for mobile ambients
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(Show Context)
Citation Context ...ckle a fully-fledged case study is the main aim of this paper. Ourstartingpointforthesynthesisofanlts are the graphical techniques proposed for modelling the reduction semantics of nominal calculi in =-=[10,12]-=-: processes are encoded in graphs with interfaces, an instance of cospan categories [11], and process reduction is simulated by double-pushout (dpo) rewriting [1]. Since the category of cospans over g... |

18 | A bi-categorical axiomatisation of concurrent graph rewriting - Gadducci, Heckel, et al. |

10 | Processes for adhesive rewriting systems
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- 2006
(Show Context)
Citation Context ... extra contexts needed to obtain the image of L in G. The mechanism was introduced in [8] in order to derive an lts from direct derivations, using bcs aslabels.The following definition is lifted from =-=[2]-=-, extending the original one by including also morphisms that are not necessarily mono. Note that the labels derived in this way correspond to the labels derived via relative pushouts in a suitable ca... |

8 | H.: Composition and decomposition of DPO transformations with borrowed context
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(Show Context)
Citation Context ... its construction was irrelevant for our purposes here, since the reuse of the interface J of the starting state does not change the bisimilarity. A related composition result is already presented in =-=[3]-=-. Finally, we consider promising the combined use of a graphical encoding (into graphs with interfaces) and of the bc techniques, and we plan to test its expressiveness by capturing also nominal calcu... |

7 | Observing reductions in nominal calculi via a graphical encoding of processes - Gadducci, Montanari - 2005 |

6 |
Multisets and structural congruence of the π-calculus with replication
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(Show Context)
Citation Context ...or ccs, namely, the axiom schema concerning the distributivity of the restriction operators with respect to the prefix operators, even if they have been already considered in the literature, see e.g. =-=[9]-=-. These equalities do not change substantially the reduction semantics, and they indeed hold in all the observational equivalences we are aware of. In particular, two congruent processes are also stro... |

6 | Deriving bisimulation congruences from reduction systems - Sobociński - 2004 |

3 | The fusion calculus: Expressiveness and simmetry in mobile processes - Parrow, Victor - 1998 |