## Proof Systems for Message-Passing Process Algebras (1993)

Venue: | Formal Aspects of Computing |

Citations: | 28 - 9 self |

### BibTeX

@INPROCEEDINGS{Hennessy93proofsystems,

author = {M. Hennessy and H. Lin},

title = {Proof Systems for Message-Passing Process Algebras},

booktitle = {Formal Aspects of Computing},

year = {1993},

pages = {379--407}

}

### OpenURL

### Abstract

We give sound and complete proof systems for a variety of bisimulation based equivalences over a message-passing process algebra. The process algebra is a generalisation of pure CCS where the actions consist of receiving and sending messages or data on communication channels; the standard prefixing operator a:p is replaced by the two operators c?x:p and c!e:p and in addition messages can be tested by a conditional construct. The various proof systems are parameterised on auxiliary proof systems for deciding on equalities or more general boolean identities over the expression language for data. The completeness of these proof systems are thus relative to the completeness of the auxiliary proof systems.

### Citations

3204 |
Communication and Concurrency
- Milner
- 1989
(Show Context)
Citation Context ...long c, depending on whether or not the value concerned is greater than or equal to 0. The standard approach to providing a semantic basis for these message{passing algebras, advocated for example in =-=[Mil89]-=-, is to translate them into an underlying pure algebra. The central feature of this translation, mapping p to [[p]], is that the input expression c?x:p is mapped into the term X v2Val c?v:[[p[v=x]]] 1... |

393 |
Algebraic Theory of Processes
- Hennessy
- 1988
(Show Context)
Citation Context ... a soundsnitary proof system is given which is also complete for recursion free processes. However all of this work is with respect to a particular behavioural equivalence called testing equivalence, =-=[Hen88]-=-. Here we wish to consider an alternative and muchsner behavioural equivalence, bisimulation equivalence from [Mil89]. The main result of the paper is a series of sound and complete proof systems, wit... |

97 |
The syntax and semantics of CRL
- Groote, Ponse
- 1994
(Show Context)
Citation Context ... our results, is described. It oers much the same functionality as the the original PAM except that message-passing process algebras can be dened and the proof elaboration scheme is moresexible. In [G=-=P90-=-] a very general language for describing message-passing, based on ACP, is described and in [GP91] a proof theory is given. Although these goals are quite similar to ours their approach is very dieren... |

19 |
A theory of communicating processes with value-passing
- Hennessy, Ingólfsdóttir
- 1990
(Show Context)
Citation Context ...nd will not be mediated by a translation into an innitary language. As a result the associated proof systems will be in some sensesnitary. Such theories already exist for value{passing processes. In [=-=HI93]-=- a fully-abstract denotational model is presented while in [Hen91] a soundsnitary proof system is given which is also complete for recursion free processes. However all of this work is with respect to... |

17 |
Automated Analysis of Mutual Exclusion Algorithms using CCS
- Walker
- 1989
(Show Context)
Citation Context ...slates message-passing processes from a language such as ours into \pure processes" which can be accepted by the Concurrency Workbench and various examples treated using this approach may be foun=-=d in [Wal89]-=-. However these approaches require the set of values to besnite and even using the boolean value space of two elements leads to an exponential blow-up in the size of descriptions. We hope that with ou... |

16 |
Proof theory for CRL
- Groote, Ponse
- 1991
(Show Context)
Citation Context ...hat message-passing process algebras can be dened and the proof elaboration scheme is moresexible. In [GP90] a very general language for describing message-passing, based on ACP, is described and in [=-=GP9-=-1] a proof theory is given. Although these goals are quite similar to ours their approach is very dierent. A modular algebraic specication language is used to describe data domains and the description... |

16 |
A Modal Logic for Message Passing Processes
- Hennessy, Liu
- 1995
(Show Context)
Citation Context ...ss theorems 4 is the notion of symbolic bisimulation equivalence. This has already been used in [HL92] to develop an algorithm for checking whether two message-passing processes are equivalent and in =-=[HL93]-=- for developing a proof system to verify that such processes satisfy properties described by formulae from asrst-order modal logic. The more standard approach to message-passing processes is to transl... |

13 |
A proof system for communicating processes with value-passing
- Hennessy
- 1991
(Show Context)
Citation Context ...ge. As a result the associated proof systems will be in some sensesnitary. Such theories already exist for value{passing processes. In [HI93] a fully-abstract denotational model is presented while in =-=[Hen91]-=- a soundsnitary proof system is given which is also complete for recursion free processes. However all of this work is with respect to a particular behavioural equivalence called testing equivalence, ... |

13 |
A Process Algebra Manipulator
- PAM
- 1992
(Show Context)
Citation Context ...nts leads to an exponential blow-up in the size of descriptions. We hope that with our approach at least some of this complexity can be avoided. In [Lin93] an extension of the PAM verication system, [=-=Lin9-=-1], based on our results, is described. It oers much the same functionality as the the original PAM except that message-passing process algebras can be dened and the proof elaboration scheme is morese... |

8 | A Verification Tool for Value-Passing Processes
- Lin
- 1993
(Show Context)
Citation Context ... and even using the boolean value space of two elements leads to an exponential blow-up in the size of descriptions. We hope that with our approach at least some of this complexity can be avoided. In =-=[Lin9-=-3] an extension of the PAM verication system, [Lin91], based on our results, is described. It oers much the same functionality as the the original PAM except that message-passing process algebras can ... |

4 |
The concurrency workbench: A semantics based veri tool for state systems
- Cleaveland, Parrow, et al.
- 1989
(Show Context)
Citation Context ...ess algebra a summation operator I where I has the same cardinality as the value domain. Such process algebras are dicult to use. For example the standard algorithms and verication tools, see e.g. [C=-=PS89-=-], do not apply and equational reasoning is dicult since any proof system based on this approach is of necessity innitary. The second disadvantage is that with such translations uniformities which exi... |

3 |
Proof Systems for message passing processes
- Hennessy, Lin
- 1996
(Show Context)
Citation Context ...x:t i This is the required (3) above. 2 Our proposed axiom schema EA is very general since it allows us to introduce an arbitrary boolean expression b into a proof. In previous versions of this work, =-=[-=-HL93], we had a dierent approach; instead of the axiom schema EA we used the following rule schema: E-INPUT b P i2I :t i = P j2J :u j b P i2I c?x:t i = P j2J c?x:u j x 62 fv(b): 16 This also is quit... |

3 | The Laws of Occam - Roscoe, Hoare - 1986 |

3 |
A calculus of mobile proceses, part i
- Milner, Parrow, et al.
- 1992
(Show Context)
Citation Context ... theoretically this quantication. Nevertheless it would be interesting to compare the two approaches. Recently, proof systems for late and early strong bisimulation equivalences over the -calculus, [M=-=PW92-=-], have been given in [PS93]. Indeed it is from this paper we have borrowed our axiom for the early version of bisimulation equivalence. At one level the - calculus may be viewed as a particular insta... |

3 |
Algebraic theories for value-passing calculi
- Parrow, Sangiorgi
- 1993
(Show Context)
Citation Context ...hese we present a corresponding proof system. In the strong cases the dierence between early and late is simply the addition of an axiom, or more correctly an axiom schema, adapted from that used in [=-=PS9-=-3] for the -calculus. On the other hand the weak version of both equivalences can be obtained by adding to the corresponding proof system the standard -laws from [Mil89]. The judgements of the proof s... |

2 |
A language for value-passing ccs
- Burns
- 1991
(Show Context)
Citation Context ... from asrst-order modal logic. The more standard approach to message-passing processes is to translate them into \pure processes" as outlined at the beginning of this section [Mil89, HR86]. Indee=-=d in [Bur91] a fr-=-ont-end for the Concurrency Workbench is described which translates message-passing processes from a language such as ours into \pure processes" which can be accepted by the Concurrency Workbench... |