## Deriving Bisimulation Congruences for Reactive Systems (2000)

Venue: | In Proc. of CONCUR 2000, 2000. LNCS 1877 |

Citations: | 117 - 14 self |

### BibTeX

@INPROCEEDINGS{Leifer00derivingbisimulation,

author = {James J. Leifer and Robin Milner},

title = {Deriving Bisimulation Congruences for Reactive Systems},

booktitle = {In Proc. of CONCUR 2000, 2000. LNCS 1877},

year = {2000},

pages = {243--258},

publisher = {Springer}

}

### Years of Citing Articles

### OpenURL

### Abstract

. The dynamics of reactive systems, e.g. CCS, has often been de ned using a labelled transition system (LTS). More recently it has become natural in de ning dynamics to use reaction rules | i.e. unlabelled transition rules | together with a structural congruence. But LTSs lead more naturally to behavioural equivalences. So one would like to derive from reaction rules a suitable LTS. This paper shows how to derive an LTS for a wide range of reactive systems. A label for an agent a is de ned 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. The key contribution of this paper is a precise de nition of \just large enough", in terms of the categorical notion of relative pushout (RPO), which ensures that bisimilarity is a congruence when sucient RPOs exist. Two examples | a simpli ed form of action calculi and term-rewriting | are given, for which it is shown that su- cient RPOs indeed exist. The thrust of thi...

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Citation Context ... has usually been operationally dened, and often centred upon an LTS; this was the case with CCS [15]. There have indeed been notable exceptions to the use of LTSs as the dening method: Hoare's CSP [1=-=2]-=- was given an elegant denotational semantics, the failures model; in the Process Algebra [3] which originated with Bergstra and Klop the emphasis was upon an algebraic theory rather than upon transiti... |

3224 |
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Citation Context ... Since the early days of process calculi, the question of behavioural equivalence has been central. It has usually been operationally dened, and often centred upon an LTS; this was the case with CCS [=-=15-=-]. There have indeed been notable exceptions to the use of LTSs as the dening method: Hoare's CSP [12] was given an elegant denotational semantics, the failures model; in the Process Algebra [3] which... |

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Citation Context ... C 0 D 0 r + (i) a D 0 r + (ii) b b 00 = E 0 r 0 + (iii) Cb C 0 b 00 = C 0 E 0 r 0 F 1 S S F 1 F 0 1 1 F 0 1 1 5(1) 0 a l C F 0 F D D 0 C 0 5(2) 0 a l F 0 D 0 5(3) C F 0 F C 0 5(4) 0 b l 0 F 0 E 0 5(5=-=-=-) 0 b l 0 C F E 0 C 0 5(6) Figure 5. Congruence proof (i) If Ca F 1 a 0 then, by denition, there exists (l; r) 2 Reacts and D 2 D such that the big rectangle in Fig. 5(2) is an IPO and a 0 = Dr. Becau... |

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Citation Context ...ns Reacts and is preserved by all contexts: l r if (l; r) 2 Reacts a a 0 Ca Ca 0 : Expanding (1) according to this denition of we have: a F a 0 i Fa a 0 i 9(l; r) 2 Reacts; D: Fa = Dl & a 0 = Dr : (2)=-=-=- The requirement Fa = Dl in (2) is rendered by a commuting a l F D square (as shown) in some category whose arrows are the agents and contexts of the reactive system. This requirement reveals thesaw d... |

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Citation Context ...became strained because the passage of names as messages required a somewhat ad hoc structure in the labels. For this reason Milner [16], inspired by the Chemical Abstract Machine of Berry and Boudol =-=-=-[4], devised an alternate semantics based upon structural congruence and reaction rules, with specic denitions of behavioural equivalence and specic congruence proofs, often based upon barbed bisimula... |

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Citation Context ...l properties [10, 24]. With the -calculus [18] the LTS methodology became strained because the passage of names as messages required a somewhat ad hoc structure in the labels. For this reason Milner [=-=1-=-6], inspired by the Chemical Abstract Machine of Berry and Boudol [4], devised an alternate semantics based upon structural congruence and reaction rules, with specic denitions of behavioural equivale... |

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Citation Context ... with Bergstra and Klop the emphasis was upon an algebraic theory rather than upon transitions. But LTSs have been prominent, and they led to an intense study of the dierent equivalences they induce [=-=9-=-], and of their congruential properties [10, 24]. With the -calculus [18] the LTS methodology became strained because the passage of names as messages required a somewhat ad hoc structure in the label... |

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Citation Context ...pon an algebraic theory rather than upon transitions. But LTSs have been prominent, and they led to an intense study of the dierent equivalences they induce [9], and of their congruential properties [=-=10, 24-=-]. With the -calculus [18] the LTS methodology became strained because the passage of names as messages required a somewhat ad hoc structure in the labels. For this reason Milner [16], inspired by the... |

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Citation Context ...n structural congruence and reaction rules, with specic denitions of behavioural equivalence and specic congruence proofs, often based upon barbed bisimulation [19]. Simultaneously, action calculi [17] were proposed as a framework embracing a wide variety of process calculi. Many calculi, including the -calculus, the - calculus, Petri nets and the Ambient calculus can be presented as action calcu... |

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Citation Context ...pon an algebraic theory rather than upon transitions. But LTSs have been prominent, and they led to an intense study of the dierent equivalences they induce [9], and of their congruential properties [=-=10, 24-=-]. With the -calculus [18] the LTS methodology became strained because the passage of names as messages required a somewhat ad hoc structure in the labels. For this reason Milner [16], inspired by the... |

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Citation Context ...r term rewriting with parallel composition. Jerey and Rathke [13] have recently studied the relationship between contextual equivalence and labelled transitions for the -calculus of Pitts and Stark [2=-=0]-=-; this will provide a good test for our uniform derivation of LTSs. We do not expect yet to achieve thesne-tuning present in some calculi; but we see no obvious limit to what can be achieved using gen... |

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Citation Context ...ing in each individual calculus. More generally, links with other lines of research must be explored. Our method does not appear to overlap with the categorical approach by Joyal, Nielsen and Winskel =-=[14-=-] in dening bisimulation from open maps, but one should attempt to integrate the categorytheoretic study of LTS-based equivalences. Categorical methods have also been productive in graph-rewriting; fo... |

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Citation Context ...orm notion of structural congruence. Thus arose the challenge tosnd a general way of deriving LTSs, and thence behavioural congruences, from reaction rules all expressed within action calculi. Sewell =-=[22]-=- has derived an LTS for several classes of reactive system, and in each case proved the induced bisimilarity to be a congruence. He also proposed a notion of colouring to keep track of component occur... |

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Citation Context ... We are at present identifying those action calculi, or subcategories thereof, which possess RPOs; this will greatly clarify the status of action calculi as a framework. In particular, sharing graphs =-=[1, 11] and -=-Gardner's closed action calculi [8] should be addressed. We also have to develop the notion of \polymorphic" context alluded to in Section 6. Calculi already equipped with LTSs and congruence pro... |

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Citation Context ... We are at present identifying those action calculi, or subcategories thereof, which possess RPOs; this will greatly clarify the status of action calculi as a framework. In particular, sharing graphs =-=[1, 11] and -=-Gardner's closed action calculi [8] should be addressed. We also have to develop the notion of \polymorphic" context alluded to in Section 6. Calculi already equipped with LTSs and congruence pro... |

36 |
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(Show Context)
Citation Context ...ion 3 about the tentative denition (1) of labelled transitions). We return to the converse property later in the special case that F is an isomorphism. Bisimulation over F 1 follows its usual scheme [=-=-=-21]: Denition 6 (bisimulation over F 1 ). Let S S m C(0; m) 2 . S is a simulationsover F 1 i for (a; b) 2 S, if a F 1 a 0 then there exists b 0 such that b F 1 b 0 and (a 0 ; b 0 ) 2 S. S is a bisimu... |

23 | Towards a theory of bisimulation for local names
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(Show Context)
Citation Context ...es come to theirs. We would like to study in generality the situation in which redexes themselves are contexts, as Sewell [22] has done for term rewriting with parallel composition. Jerey and Rathke [=-=13-=-] have recently studied the relationship between contextual equivalence and labelled transitions for the -calculus of Pitts and Stark [20]; this will provide a good test for our uniform derivation of ... |

15 |
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Citation Context ...t one should attempt to integrate the categorytheoretic study of LTS-based equivalences. Categorical methods have also been productive in graph-rewriting; for example, in 1991 Corradini and Montanari =-=[6]-=- were already combining categorical and algebraic methods in concurrent graphrewriting. Such work has developed further and should be related to ours. In the longer term, we believe that graphical mod... |

11 |
A Calculus of Mobile Processes part 1
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Citation Context ... than upon transitions. But LTSs have been prominent, and they led to an intense study of the dierent equivalences they induce [9], and of their congruential properties [10, 24]. With the -calculus [1=-=8]-=- the LTS methodology became strained because the passage of names as messages required a somewhat ad hoc structure in the labels. For this reason Milner [16], inspired by the Chemical Abstract Machine... |

5 | Closed action calculi
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(Show Context)
Citation Context ...calculi, or subcategories thereof, which possess RPOs; this will greatly clarify the status of action calculi as a framework. In particular, sharing graphs [1, 11] and Gardner's closed action calculi =-=[8] shou-=-ld be addressed. We also have to develop the notion of \polymorphic" context alluded to in Section 6. Calculi already equipped with LTSs and congruence proofs need to be checked to see how close ... |