## Probabilistic Simulations for Probabilistic Processes (1994)

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Citations: | 265 - 18 self |

### BibTeX

@MISC{Segala94probabilisticsimulations,

author = {Roberto Segala and Nancy Lynch},

title = {Probabilistic Simulations for Probabilistic Processes},

year = {1994}

}

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### Abstract

Several probabilistic simulation relations for probabilistic systems are defined and evaluated according to two criteria: compositionality and preservation of "interesting" properties. Here, the interesting properties of a system are identified with those that are expressible in an untimed version of the Timed Probabilistic concurrent Computation Tree Logic (TPCTL) of Hansson. The definitions are made, and the evaluations carried out, in terms of a general labeled transition system model for concurrent probabilistic computation. The results cover weak simulations, which abstract from internal computation, as well as strong simulations, which do not.

### Citations

3204 |
Communication and Concurrency
- Milner
- 1989
(Show Context)
Citation Context ...systems. In the non-probabilistic setting, labeled transition systems have become well accepted as a basis for formal specification and verification of concurrent and distributed systems. (See, e.g., =-=[16, 17]-=-.) A transition system is an abstract machine that represents either an implementation (i.e., a physical device or software system), or a specification (i.e., a description of the required properties ... |

493 | Algebraic laws for nondeterminism and concurrency - Hennessy, Milner - 1985 |

403 | Bisimulation through probabilistic testing
- Larsen, Skou
- 1991
(Show Context)
Citation Context ... WPCTL. Intuitively, the main reason for this result is that PCTL and WPCTL are concerned with probability bounds rather than exact probabilities. We then redefine the strong bisimulation relation of =-=[7, 13]-=- in terms of our model, and also define a strong simulation relation that generalizes the simulation relation of [11], strengthening it a bit so that some liveness is preserved. We show that strong si... |

393 | Algebraic Theory of Processes - Hennessy - 1988 |

366 | Hierarchical correctness proofs for distributed algorithms
- Lynch, Tuttle
- 1987
(Show Context)
Citation Context ...gebraic setting. Unidirectional simulations, such as refinement mappings and forward simulations, have turned out to be quite successful in formal verification of nonprobabilistic distributed systems =-=[10, 15, 16]-=-. Thus, it is highly desirable to extend the use of simulations to the probabilistic setting. ? Supported by NSF grant CCR-89-15206, and CCR-92-25124, by DARPA contracts N0001489 -J-1988 and N00014-92... |

255 | Branching Time and Abstraction in Bisimulation Semantics
- Glabbeek, Weijland
- 1996
(Show Context)
Citation Context ...s reason we introduce other two relations, called branching probabilistic bisimulation and branching probabilistic simulation, which impose new restrictions similar to those of branching bisimulation =-=[6]-=-. Our third main result is that branching probabilistic bisimulation and branching probabilistic simulation are compositional and preserve PCTL formulas and PCTL formulas without negation and existent... |

215 |
Automatic verification of probabilistic concurrent finite state programs
- Vardi
- 1985
(Show Context)
Citation Context ... order to extend labeled transition systems to the probabilistic setting, the main addition that is needed is some mechanism for representing probabilistic choices as well as nondeterministic choices =-=[7, 19, 21]-=-. In the non-probabilistic setting, there are two principal methods that are used for analyzing labeled transition systems: temporal logic (e.g. [18]), which is used to establish that a system satisfi... |

196 |
Another advantage of free choice: Completely asynchronous agreement protocols
- Ben-Or
- 1983
(Show Context)
Citation Context ...ch abstract from internal computation, as well as strong simulations, which do not. 1 Introduction Randomization has been shown to be a useful tool for the solution of problems in distributed systems =-=[1, 2, 12]-=-. In order to support reasoning about probabilistic distributed systems, many researchers have recently focused on the study of models and methods for the analysis of such systems [3, 5, 7, 19--21]. T... |

152 | Reactive, generative, and stratified models of probabilistic processes
- Glabbeek, Smolka, et al.
- 1995
(Show Context)
Citation Context ...ilistic schedulers. A fully probabilistic automaton is a probabilistic automaton without nondeterminism; at each point only one step can be chosen.. The generative model of probabilistic processes of =-=[5]-=- is a special case of a fully probabilistic automaton; simple probabilistic automata are partially captured by the reactive model of [5] in the sense that the reactive model assumes some form of nonde... |

147 |
Time and probability in formal design of distributed systems
- Hansson
- 1994
(Show Context)
Citation Context ... order to extend labeled transition systems to the probabilistic setting, the main addition that is needed is some mechanism for representing probabilistic choices as well as nondeterministic choices =-=[7, 19, 21]-=-. In the non-probabilistic setting, there are two principal methods that are used for analyzing labeled transition systems: temporal logic (e.g. [18]), which is used to establish that a system satisfi... |

147 |
Temporal Semantics of Concurrent Programs
- Pnueli
- 1981
(Show Context)
Citation Context ...choices as well as nondeterministic choices [7, 19, 21]. In the non-probabilistic setting, there are two principal methods that are used for analyzing labeled transition systems: temporal logic (e.g. =-=[18]), which i-=-s used to establish that a system satisfies certain properties, and equivalence or preorder relations (e.g., [8, 16, 17]), which are used to establish that one system "implements" another, a... |

128 | Fast randomized consensus using shared memory
- Aspnes, Herlihy
- 1990
(Show Context)
Citation Context ...ch abstract from internal computation, as well as strong simulations, which do not. 1 Introduction Randomization has been shown to be a useful tool for the solution of problems in distributed systems =-=[1, 2, 12]-=-. In order to support reasoning about probabilistic distributed systems, many researchers have recently focused on the study of models and methods for the analysis of such systems [3, 5, 7, 19--21]. T... |

96 |
Specification and refinement of probabilistic processes
- Jonsson, Larsen
- 1991
(Show Context)
Citation Context ... than exact probabilities. We then redefine the strong bisimulation relation of [7, 13] in terms of our model, and also define a strong simulation relation that generalizes the simulation relation of =-=[11]-=-, strengthening it a bit so that some liveness is preserved. We show that strong simulation preserves PCTL formulas without negation and existential quantification, and we show that the kernel of stro... |

78 |
On the advantages of free choice: A symmetric and fully distributed solution to the dining philosophers problem
- Rabin, Lehmann
- 1981
(Show Context)
Citation Context ... ; P 2 ) = D(s 2 ). ut 3.2 Schedulers and Adversaries Several papers in the literature use schedulers, sometimes viewed as adversarial entities, to resolve the nondeterminism in probabilistic systems =-=[4, 7, 14, 21]-=-. An adversary is an object that schedules the next step based on the past history of a probabilistic automaton. Definition6. An adversary for a probabilistic automaton M is a function A taking a fini... |

63 | Forward and backward simulations for timingbased systems
- Lynch, Vaandrager
- 1991
(Show Context)
Citation Context ...systems. In the non-probabilistic setting, labeled transition systems have become well accepted as a basis for formal specification and verification of concurrent and distributed systems. (See, e.g., =-=[16, 17]-=-.) A transition system is an abstract machine that represents either an implementation (i.e., a physical device or software system), or a specification (i.e., a description of the required properties ... |

60 | Time-optimal self stabilizing spanning tree algorithms - Aggarwal, Kutten - 1989 |

52 | Composition and behaviors of probabilistic I/O automata - Wu, Smolka, et al. - 1997 |

51 |
Verification of Multiprocess Proba-bilistic Protocols
- Pnueli, Zuck
- 1986
(Show Context)
Citation Context ... order to extend labeled transition systems to the probabilistic setting, the main addition that is needed is some mechanism for representing probabilistic choices as well as nondeterministic choices =-=[7, 19, 21]-=-. In the non-probabilistic setting, there are two principal methods that are used for analyzing labeled transition systems: temporal logic (e.g. [18]), which is used to establish that a system satisfi... |

37 | Probabilistic communicating processes - Seidel - 1995 |

36 | Concurrency and automata on in sequences - Park - 1981 |

34 | Proving time bounds for randomized distributed algorithms - Lynch, Saias, et al. |

32 |
Simulations between specifications of distributed systems
- Jonsson
- 1991
(Show Context)
Citation Context ...gebraic setting. Unidirectional simulations, such as refinement mappings and forward simulations, have turned out to be quite successful in formal verification of nonprobabilistic distributed systems =-=[10, 15, 16]-=-. Thus, it is highly desirable to extend the use of simulations to the probabilistic setting. ? Supported by NSF grant CCR-89-15206, and CCR-92-25124, by DARPA contracts N0001489 -J-1988 and N00014-92... |

29 | Modelling and veri of randomized distributed real-time systems - Segala - 1995 |

20 | Branching time and abstraction in bisimulation semantics - Glabbeek, Weijland - 1996 |

19 | Reactive, generative and strati models of probabilistic processes - Glabbeek, Steen, et al. - 1990 |

18 | Testing Equivalences for Probabilistic Processes - Christoff - 1990 |

16 | Randomized mutual exclusion algorithms revisited - Kushilevitz, Rabin - 1992 |

12 |
Reasoning about uncertainty in fault-tolerant distributed systems
- Fischer, Zuck
- 1988
(Show Context)
Citation Context ... ; P 2 ) = D(s 2 ). ut 3.2 Schedulers and Adversaries Several papers in the literature use schedulers, sometimes viewed as adversarial entities, to resolve the nondeterminism in probabilistic systems =-=[4, 7, 14, 21]-=-. An adversary is an object that schedules the next step based on the past history of a probabilistic automaton. Definition6. An adversary for a probabilistic automaton M is a function A taking a fini... |

7 | Speci and re of probabilistic processes - Jonsson, Larsen - 1991 |

2 | Simulations between Speci of Distributed Systems - Jonsson - 1991 |

2 | Automatic Veri of Probabilistic Concurrent FiniteState Programs - Vardi - 1985 |

1 | Three Logics for Branching Bisimulation (extended abstract - Nicola, W - 1990 |