## Probability and Nondeterminism in Operational Models of Concurrency (2006)

Venue: | In Proc. CONCUR, LNCS |

Citations: | 12 - 1 self |

### BibTeX

@INPROCEEDINGS{Segala06probabilityand,

author = {Roberto Segala},

title = {Probability and Nondeterminism in Operational Models of Concurrency},

booktitle = {In Proc. CONCUR, LNCS},

year = {2006},

pages = {64--78},

publisher = {Springer}

}

### OpenURL

### Abstract

Abstract. We give a brief overview of operational models for concurrent systems that exhibit probabilistic behavior, focussing on the interplay between probability and nondeterminism. Our survey is carried out from the perspective of probabilistic automata, a model originally developed for the analysis of randomized distributed algorithms. 1

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Citation Context ...of probabilistic automata. A good understanding of the relationship between these models is still open. We mention also the interesting approach to performance evaluation of Interactive Markov Chains =-=[23]-=-. In this case actions are immediate and time is described by explicit transitions with exponential delays. The advantage of this approach is that it is possible to keep nondeterminism in the model. 3... |

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Citation Context ...ulations Simulation and bisimulation relations are attractive for their mathematical simplicity. They have been studied extensively in the context of probabilistic systems, including reactive systems =-=[26]-=-, alternating models [21, 32, 2], and non alternating models [36, 4]. The existing definitions are very different in style; however, as shown in [37], all the proposals end up being equivalent once we... |

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Citation Context ...es, while in the labeled generative case we obtain Markov processes with actions. These models are used mainly for performance evaluation and are studied in the context of stochastic process algebras =-=[20, 24, 6]-=-. The underlying idea is that actions describe resources that are available with exponentially distributed delays, which means that there is a close correspondence between the delay parameter of the a... |

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Citation Context ...he weak relations. Indeed, it turns out that the non-probabilistic versions of the weak relations are not transitive [14]. A definition of weak bisimulation is proposed also for the alternating model =-=[33]-=- using deterministic schedulers. The definition uses conditional probability measures and is given in a very different style compared to this paper; however, our definition of weak probabilistic bisim... |

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Citation Context ...isimulation relations are attractive for their mathematical simplicity. They have been studied extensively in the context of probabilistic systems, including reactive systems [26], alternating models =-=[21, 32, 2]-=-, and non alternating models [36, 4]. The existing definitions are very different in style; however, as shown in [37], all the proposals end up being equivalent once we see the alternating models as s... |

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Citation Context ...n of [32]. 4.5 Other kinds of Bisimulations Bisimulation relations are studied extensively also in pure probabilistic models. The definitional style is very similar to ours and we refer the reader to =-=[3]-=- for an extensive comparative study. In particular in the absence of nondeterminism several relations coincide. There are also several variations of simulation and bisimulation relations in the litera... |

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Citation Context ...lues of the shared variables (e.g., the values of some variables are under the control of a single component). A successful attempt to solve the synchronization problem in unlabeled models appears in =-=[13]-=-, where a probabilistic extension of reactive modules [1] is studied. Example 5. Consider two unlabeled probabilistic automata A1, A2 whose states include a variable X. Suppose that A1 from its initia... |

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Citation Context ...el. In [4] there is a proposal for a probabilistic version of normed bisimulation which has the advantage of being decidable efficiently. Indeed, strong bisimulations are decidable in polynomial time =-=[8]-=-, while weak bisimulations are decidable in exponential time on probabilistic automata [8]. Interestingly, though, weak bisimulations are decidable in polynomial time in the alternating model [32] sin... |

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Citation Context ... investigate further. Within the field of domain theory and denotational semantics, several models have been proposed that combine probability and nondeterminism. The interested reader may start from =-=[38, 11]-=- for more details. There has been also extensive research on probabilistic extensions of guarded command languages and their applications. The interested reader is referred to [28].sOur overview is gi... |

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Citation Context ... component. Another advantage of the input/output distinction is that it is possible to consider PIOAs with generative locally controlled transitions, and yet define a meaningful composition operator =-=[40, 35]-=-. Indeed, the transitions of a composition can be obtained either by synchronizing input transitions, or by synchronizing a locally controlled transition of one component with appropriate input trans... |

12 | Stochastic transition systems for continuous state spaces and non-determinism
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Citation Context ...n-discrete measures poses non-trivial measurability problems that go beyond the scope of this paper. We refer the reader to [30, 18] for an understanding of the problem on deterministic models and to =-=[9]-=- for an understanding of the problem in the presence of nondeterminism. 4 Simulations and Bisimulations Simulation and bisimulation relations are attractive for their mathematical simplicity. They hav... |

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Citation Context ...ere is a vast literature on timed extension of probabilistic models. We have described before some ways to associate delays with actions and we refer the interested reader to a survey that appears in =-=[7]-=-. In the context of probabilistic automata one possibility to deal with time is by adding explicit time-passage transitions to the model and keep the underlying theory unchanged. This is done already ... |

10 |
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Citation Context ... automata, schedulers can only be discrete. A treatment of real-time with non-discrete measures poses non-trivial measurability problems that go beyond the scope of this paper. We refer the reader to =-=[30, 18]-=- for an understanding of the problem on deterministic models and to [9] for an understanding of the problem in the presence of nondeterminism. 4 Simulations and Bisimulations Simulation and bisimulati... |

8 | Switched probabilistic I/O automata, in
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Citation Context .../O automata, including the task mechanisms used to describe fairness properties and the ability to use language inclusion to preserve fairness properties as well. A probabilistic I/O automaton (PIOA) =-=[10]-=- is a probabilistic automaton whose external actions are partitioned into input and output actions such that for each state q and each input action a there is at least one transition labeled by a enab... |

7 | C.: Branching bisimulation for probabilistic systems: Characteristics and decidability
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Citation Context ...isimulation relations are attractive for their mathematical simplicity. They have been studied extensively in the context of probabilistic systems, including reactive systems [26], alternating models =-=[21, 32, 2]-=-, and non alternating models [36, 4]. The existing definitions are very different in style; however, as shown in [37], all the proposals end up being equivalent once we see the alternating models as s... |

7 |
Distributing probability over nondeterminism Mathematical Structures in Computer Science archive Volume 16
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Citation Context ... investigate further. Within the field of domain theory and denotational semantics, several models have been proposed that combine probability and nondeterminism. The interested reader may start from =-=[38, 11]-=- for more details. There has been also extensive research on probabilistic extensions of guarded command languages and their applications. The interested reader is referred to [28].sOur overview is gi... |

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Comparative analysis of bisimulation relations on alternating and non-alternating probabilistic models
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Citation Context ...ts of the least expressive model into objects of the other model so that bisimilarity is preserved and reflected. The transformations should preserve states; thus, for example, the transformations of =-=[37]-=- are not acceptable since they add or remove probabilistic states. Indeed, the alternating and non-alternating models are incomparable according to [5]. We have omitted here any reference to process a... |

4 | Axiomatization of trace semantics for stochastic nondeterministic processes
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Citation Context ...omparable according to [5]. We have omitted here any reference to process algebras, axiomatizations and logical characterizations for probabilistic models. For process algebras the reader may look at =-=[31]-=- and references therein, while for logical characterizations the reader may look at [26, 17]. The work in [17] is carried out in the context of alternating non-discrete systems and improves the result... |

3 |
Norm functions for bisimulations with delays
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Citation Context ... their mathematical simplicity. They have been studied extensively in the context of probabilistic systems, including reactive systems [26], alternating models [21, 32, 2], and non alternating models =-=[36, 4]-=-. The existing definitions are very different in style; however, as shown in [37], all the proposals end up being equivalent once we see the alternating models as special instances of probabilistic au... |

3 |
Axiomatisations and types for probabilistic and mobile processes
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Citation Context ...generate weak transitions, we have defined directly the probabilistic versions of the weak relations. Indeed, it turns out that the non-probabilistic versions of the weak relations are not transitive =-=[14]-=-. A definition of weak bisimulation is proposed also for the alternating model [33] using deterministic schedulers. The definition uses conditional probability measures and is given in a very differen... |