## Representing Nondeterministic and Probabilistic Behaviour in Reactive Processes (1993)

Citations: | 20 - 0 self |

### BibTeX

@TECHREPORT{Lowe93representingnondeterministic,

author = {Gavin Lowe},

title = {Representing Nondeterministic and Probabilistic Behaviour in Reactive Processes},

institution = {},

year = {1993}

}

### OpenURL

### Abstract

. In this paper we investigate ways of modelling communicating processes that display both nondeterministic and probabilistic behaviour. We present an operational model for a probabilistic version of CSP, and describe a number of ways of abstracting a denotational semantics from such a model, so as to represent a process by a set of probability functions, one function for each way of resolving the nondeterministic choices. We then prove an interesting--- although disappointing---result, which shows that no such denotational model can be compositional. We end by identifying a problem with the operational model, which is shared by all similar models known to us, and briefly give some indications as to how this problem might be overcome. 1. Introduction In recent years, an important problem in the study of communicating systems has been the modelling of probabilistic behaviour. This is necessary if we are to argue formally about unreliable behaviour (for example that displayed by an unre...

### Citations

3604 | Communicating Sequential Processes
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- 1978
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Citation Context ... operational model can suitably model such processes. Most previous semantic models for probabilistic behaviour have been opera1 In this paper we will be using a probabilistic language based upon CSP =-=[Hoa85]-=-, which we will formally define in section 4. However, a corresponding analysis could be applied to any similar process algebra. Representing Nondeterministic and Probabilistic Behaviour in Reactive P... |

3383 |
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- 1990
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Citation Context ...nting Nondeterministic and Probabilistic Behaviour in Reactive Processes 3 tional in nature. We briefly review here what we believe to be some of the more important contributions. Van Glabbeek et al. =-=[vGSST90]-=- discuss reactive, generative and stratified models of probabilistic processes. ffl They define a reactive model to be one where the environment may only offer one event at a time. If the process can ... |

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- 1986
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Citation Context ...\Gamma! STOP u (b \Gamma! STOP \Gamma c \Gamma! STOP) which has an obvious representation as an NPA graph. However this rule does not hold in more sophisticated models, such as the ready-set model of =-=[OH86]-=-. The point is that in the failures model, this instability can be modelled as nondeterminism, whereas this is not possible in other models. To get round this, it may be possible to model this instabi... |

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Citation Context ...ilistic processes, and argued that they did not: nondeterministic choices should be made independently of any other branching, and so really need to be made before any other branching. Jou and Smolka =-=[JS90]-=- have considered various equivalences for probabilistic processes using the generative model, i.e. with external probabilistic choices. They extend the notions of trace [Hoa85], failure [BHR84], ready... |

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- 1992
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Citation Context ... it identifies [p]P fi + [1 \Gamma p]P with P (where fi + is a probabilistic choice operator). Representing Nondeterministic and Probabilistic Behaviour in Reactive Processes 5 Wang Yi and Kim Larsen =-=[YL92]-=- also describe a testing semantics for a probabilistic language, and define preorders v must , v may and v test , analogous to Strulo's v u , v l and v c , respectively. Our approach in this paper has... |

49 |
Refusal testing
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- 1987
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Citation Context ...ndeterminism, whereas this is not possible in other models. To get round this, it may be possible to model this instability in some other way, for example as in the refusal testing models of Phillips =-=[Phi86]-=- and Mukarram [Muk93]. However, the above syntax will be enough for our purposes. 4.2. Subsidiary functions Before giving an operational semantics for our language in terms of NPA graphs, we need to d... |

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- 1995
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Citation Context ...essiveness in Seidel's case, and added complexity in mine. I believe that by allowing nondeterministic behaviour, this paper makes a contribution to avoiding these problems. More recently, Ben Strulo =-=[Str93]-=- has proposed an operational model for a timed language with both probabilistic and nondeterministic behaviours. He defines three sorts of transitions: action, probabilistic, and timed. He defines str... |

39 |
and branching structures in the semantics and logics of reactive systems
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18 |
Testing Equivalences for Probabilistic Processes
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Citation Context ...lta \Delta \Delta \Deltaff 0 :3 A A A AU 0 :7 t ? b t t ? c t d \Delta \Delta \Delta \Deltaff 0 :3 A A A AU 0 :7 t ? a t ? a t ? b t ? c t t Jou and Smolka's work is based upon broom tests. Christoff =-=[Chr90]-=- extends this to barb tests and defines a number of equivalences based on these tests. However I don't think it is possible to adapt these equivalences to NPA graphs, because they depend heavily upon ... |

7 |
Pravda: A Tool for Verifying Probabilistic Processes
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Citation Context ...or Q , i.e. Q is more predictable than P . I believe that the methods developed in this paper will prove useful in the verification of probabilistic systems. I am currently developing a tool---Pravda =-=[Low93a]-=----which tests for refinement between processes, as formally defined in this paper. I believe that this gives an intuitively clear way of specifying probabilistic processes. For example, consider the ... |

5 |
A theory of CSP
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- 1978
(Show Context)
Citation Context ... from an NPA graph. This will allow us to define the notions of equivalence and refinement between NPA graphs. By considering various sorts of "observations"---for example traces [Hoa85] and=-= failures [BHR84]-=----we can define various different denotational models, and thus different equivalences. We illustrate these ideas by applying them to a probabilistic language based upon CSP [Hoa85]. We describe how ... |

5 |
A Refusal Testing Model for CSP. D
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- 1993
(Show Context)
Citation Context ... this is not possible in other models. To get round this, it may be possible to model this instability in some other way, for example as in the refusal testing models of Phillips [Phi86] and Mukarram =-=[Muk93]-=-. However, the above syntax will be enough for our purposes. 4.2. Subsidiary functions Before giving an operational semantics for our language in terms of NPA graphs, we need to define a few subsidiar... |

1 |
On the faithfulness of formal modals
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- 1991
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Citation Context ... Probabilistic Behaviour in Reactive Processes 25 6. On the faithfulness of the operational semantics In this section we discuss to what extent our operational representation of processes is faithful =-=[MP91]-=- to our informal understanding of nondeterministic and probabilistic behaviour. It is instructive to consider what algebraic laws one might expect to hold in our language. One might expect most of the... |