## A distribution law for CCS and a new congruence result for the pi-calculus (2007)

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Venue: | In Proc. of FoSSaCS’07, volume 4423 of LNCS |

Citations: | 3 - 1 self |

### BibTeX

@INPROCEEDINGS{Hirschkoff07adistribution,

author = {Daniel Hirschkoff and Damien Pous},

title = {A distribution law for CCS and a new congruence result for the pi-calculus},

booktitle = {In Proc. of FoSSaCS’07, volume 4423 of LNCS},

year = {2007},

pages = {228--242},

publisher = {Springer}

}

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### Abstract

Abstract. We give an axiomatisation of strong bisimilarity on a small fragment of CCS that does not feature the sum operator. This axiomatisation is then used to derive congruence of strong bisimilarity in the finite π-calculus in absence of sum. To our knowledge, this is the only nontrivial subcalculus of the π-calculus that includes the full output prefix and for which strong bisimilarity is a congruence.

### Citations

435 |
The π-calculus: A Theory of Mobile Processes
- Sangiorgi, Walker
- 2001
(Show Context)
Citation Context ...bisimilarity [12], which has a more involved definition than the early and late variants. Tools like the Mobility Workbench [14], for instance, have adopted this equivalence on processes. It is known =-=[13]-=- that bisimilarity in the π-calculus fails to be a congruence as soon as we have prefix, parallel composition, restriction and replication. In this work, we focus on the finite, sum-free π-calculus, t... |

154 |
Symbolic bisimulations
- Hennessy, Lin
- 1995
(Show Context)
Citation Context ... semantics, for which concurrency cannot be reduced to nondeterminism, are more likely to be substitution closed: we prove that this is the case for Castellani and Hennessy’s distributed bisimilarity =-=[5]-=- in µCCS extended with choice. Coming back to the π-calculus, we exploit a transfer property that allows us to derive from the absence of mutual desynchronisations in µCCS the same result in π0, the f... |

65 |
A theory of bisimulation for the π-calculus
- Tiu, Sangiorgi, et al.
- 1996
(Show Context)
Citation Context ...ay, but it also helps making bisimulation proofs simpler, by reducing the size of case analyses. In the full π-calculus, in order to get congruence, one has to work with Sangiorgi’s open bisimilarity =-=[12]-=-, which has a more involved definition than the early and late variants. Tools like the Mobility Workbench [14], for instance, have adopted this equivalence on processes. It is known [13] that bisimil... |

50 | Axioms for Concurrency - Moller - 1989 |

28 | Finite equational bases in process algebra: Results and open questions
- Aceto, Fokkink, et al.
(Show Context)
Citation Context ...eft-hand side process with the right-hand side process. Remark 1.1 (On the distribution law and PA). Among the studies about properties of ∼ in process algebras that include parallel composition (see =-=[1]-=- for a recent survey on axiomatisations), some works focus on calculi where parallel composition is treated as a primitive operator (as opposed to being expressible using sum or other constructs like ... |

28 | Bisimulation equivalence is decidable for normed process algebra
- Hirshfeld, Jerrum
- 1999
(Show Context)
Citation Context ...is a prefixed process, then it is prime. This idea is used in the proof of Lemma 2.5. We first establish a technical result, that essentially exploits the same argument as the proof of Theorem 4.2 in =-=[7]-=-. Lemma 2.4. If η.P ∼ Q | Q ′ ,withQ, Q ′ �∼ 0, then there exist A and k>1 such that η.P ∼ (η.A) k and η.A is a normal form. Proof. By Lemma 1.6, we have η.P ∼ n(Q | Q ′ ). Furthermore, we have that n... |

24 |
Unique decomposition of processes
- Milner, Moller
- 1993
(Show Context)
Citation Context ... (∼) between processes is then equivalent to equality of their normal forms. This rewriting phase allows us to actually compute unique decompositions of processes into prime processes, inthe sense of =-=[10]-=-: a process P is prime if P is not bisimilar to the inactive process 0 and if P ∼ Q | R implies Q ∼ 0 or R ∼ 0. The distribution law is an equational schema, corresponding to an infinite family of axi... |

19 |
Verification over Infinite States
- Burkart, Caucal, et al.
- 2001
(Show Context)
Citation Context ...osition has been established for a variety of process algebras, and used as a way to prove decidability of behavioural equivalence and to give complexity bounds for the associated decision procedure (=-=[9,3]-=- cite relevant references). In the present study, beyond the existence of a unique decomposition, we are interested in a syntactic characterisation of ∼ (which will in particular allow us to derive Le... |

15 |
Bisimulations for Concurrency
- Castellani
- 1988
(Show Context)
Citation Context ...sses (and hence more discriminating than ∼), to be closed under substitution. There are several approaches to define such equivalences. We focus here on a version of (strong) distributed bisimilarity =-=[5, 4]-=-, because it is among the simplest, and this will suffice for our purposes. The definition of distributed bisimilarity relies on distributed transitions, which are given by judgements of the form P µ ... |

13 |
An ω-complete equational specification of interleaving
- Fokkink, Luttik
- 2000
(Show Context)
Citation Context ...ator is a general form of sequential composition. This equality is valid in [8] whenever η is a ‘monomorphic process’, meaning that η can only reduce to 0 (which corresponds to μCCS), or to η itself. =-=[6]-=- presents a finite axiomatisation of PA that exploits the operators of sum and left merge. Lemma 1.5. The relation � is strongly normalising and confluent. Proof. If P � P ′ then the weight of P ′ (de... |

9 |
Some Congruence Properties for π-calculus Bisimilarities
- Boreale, Sangiorgi
- 1998
(Show Context)
Citation Context ... ground, early, late and open bisimilarities coincide, and are congruences. The problem of congruence of ∼g on π0 is mentioned as an open question in [13, Chapter 5], and is known since at least 1998 =-=[2]-=-. To our knowledge, this is the first congruence result for a subcalculus of the π-calculus that includes the full output prefix (see Section 5 for a discussion on this). At the heart of our proof of ... |

6 |
A new strategy for proving ω-completeness applied to process algebra
- Groote
- 1990
(Show Context)
Citation Context ...ω N, whenever for any ground instantiation ρ, it holds that Mρ ∼ Nρ. An equation M = N is said to be correct if M ∼ω N. Our proof of ω-completeness essentially relies on the methodology developped in =-=[8]-=-; the idea is to replace variables by small terms that can easily be distinguished. Lemma 3.4. Let M be a term whose variables all belong to {Xi}i∈I, and let {ai}i∈I be a collection of distinct names ... |

1 |
Handbook of Process Algebra, chapter Process Algebras with Localities
- Castellani
- 2001
(Show Context)
Citation Context ...k in Pπ, which cannot identify two names. The question of substitution closure can also be raised in the framework of location sensitive behavioural equivalences such as distributed bisimilarity (see =-=[4]-=-). Without having a formal proof for this claim, we expect this equivalence to be substitution closed on restriction-free CCS. We believe this should be the case because in absence of restriction, dis... |

1 |
Towards parallelization of concurrent systems. Informatique Théorique et Applications
- Corradini, Gorrieri, et al.
- 1998
(Show Context)
Citation Context ...yond the existence of a unique decomposition, we are interested in a syntactic characterisation of ∼ (which will in particular allow us to derive Lemma 4.6 below). In this sense, our work is close to =-=[5]-=-, where the notion of maximally parallel process in CCS (with choice) is studied. [5] defines a rewriting process through which maximally parallel normal forms can be computed, and shows that in the c... |

1 |
What is Algebraic
- Luttik
(Show Context)
Citation Context ...osition has been established for a variety of process algebras, and used as a way to prove decidability of behavioural equivalence and to give complexity bounds for the associated decision procedure (=-=[9,3]-=- cite relevant references). In the present study, beyond the existence of a unique decomposition, we are interested in a syntactic characterisation of ∼ (which will in particular allow us to derive Le... |

1 |
The Mobility Workbench. available from http://www.it.uu.se/research/group/mobility/mwb
- Victor, Moller, et al.
- 2006
(Show Context)
Citation Context ...calculus, in order to get congruence, one has to work with Sangiorgi’s open bisimilarity [12], which has a more involved definition than the early and late variants. Tools like the Mobility Workbench =-=[14]-=-, for instance, have adopted this equivalence on processes. It is known [13] that bisimilarity in the π-calculus fails to be a congruence as soon as we have prefix, parallel composition, restriction a... |