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## A Denotational Model for Probabilistic and Nondeterministic Processes (2000)

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### Citations

528 | Bisimulation through Probabilistic Testing.
- Larsen, Skou
- 1991
(Show Context)
Citation Context ...terministic processes. The alternating of both kinds of processes is necessary, this is why the model is called alternatingsmodel. Besides the models already mentioned, several languages based on CCS =-=[4, 11, 13]-=- that analyze several semantic aspects have been proposed. Thus, in [13] a notion of bisimulation between probabilistic transition systems is introduced; this topic is also studied in [4]. In [11] sev... |

444 |
Algebraic Theory of Processes
- Hennessy
- 1988
(Show Context)
Citation Context ...mpotence for both choices is fully maintained, and then, our model is a full extension of EPL. The paper is structured as follows. Section 2 presents the syntax of the language as an extension of EPL =-=[9-=-]. In Section 3 we present an operational semantics for the whole language. In Section 4 a testing semantics is presented. In Section 5 a denotational semantics is given for a nite version of the lang... |

114 | Algebraic reasoning for probabilistic concurrent systems
- Giacalone, Jou, et al.
- 1990
(Show Context)
Citation Context ...posed including time, priorities and probabilities. One of the rst papers describing processes with a probabilistic behaviour is [2], where the concept of probabilistic experiments is introduced. In [=-=7-=-] PCCS is dened as an algebraic language based on the synchronous version of CCS where the nondeterministic choice is replaced by a probabilistic choice: P [p i ]E i , where p i is the probability the... |

103 |
A calculus for communicating systems with time and probabilities
- Hansson
- 1991
(Show Context)
Citation Context ...e CICYT project Formal development of distributed systems, TIC97-0669-c03-02. three interpretations for concurrent probabilistic processes are presented: reactive, generative and stratied models. In [=-=8]-=- TPCCS is presented, which is an extension of CCS with probabilities and time. This model is based on the asynchronous version of CCS and allows us to model more realistic concurrent systems, which ar... |

89 |
Equivalences, Congruences, and Complete Axiomatizations for Probabilistic Processes. In:
- Jou, Smolka
- 1990
(Show Context)
Citation Context ...terministic processes. The alternating of both kinds of processes is necessary, this is why the model is called alternatingsmodel. Besides the models already mentioned, several languages based on CCS =-=[4, 11, 13]-=- that analyze several semantic aspects have been proposed. Thus, in [13] a notion of bisimulation between probabilistic transition systems is introduced; this topic is also studied in [4]. In [11] sev... |

71 |
Testing probabilistic and nondeterministic processes.
- Yi, Larsen
- 1992
(Show Context)
Citation Context ...tween two processes). This is why we need a language that allows us to model nondeterministic systems 1 with or without quantication, depending on the nature of the system. Following these ideas, in [=-=18-=-] a probabilistic extension of CCS is presented. The language adds a probabilistic choice operator ( p ) indexed with a probability p 2 (0; 1), which models the probabilistic internal choice, whereas ... |

57 | Testing preorders for probabilistic processes can be characterized by simulations. - Jonsson, Wang - 2002 |

44 | Refinement-oriented probability for CSP. - Morgan, McIver, et al. - 1996 |

36 | Process Algebra with Probabilistic Choice”,
- Andova
- 1999
(Show Context)
Citation Context ...hat maintains nondeterminism. In order to deal with probabilities and nondeterminism we need to choose which of the two choices (probabilistic or internal choice) has to be resolved rst. Some models [=-=1, 15, 18-=-] consider that probabilistic choice is resolved rst, whereas other models [14] consider the opposite approach. A different point of view is considered in [12], where an actionguarded reactive probabi... |

29 | A testing equivalence for reactive probabilistic processes.
- Kwiatkowska, Norman
- 1998
(Show Context)
Citation Context ... to be resolved rst. Some models [1, 15, 18] consider that probabilistic choice is resolved rst, whereas other models [14] consider the opposite approach. A different point of view is considered in [1=-=-=-2], where an actionguarded reactive probabilistic choice is introduced and the point at which probabilistic choice occurs has no signicance. The decision of which choice is made rst is very important ... |

24 | Representing nondeterministic and probabilistic behaviour in reactive processes.
- Lowe
- 1993
(Show Context)
Citation Context ... in the testing theory of De Nicola and Hennessy. This work is extended in [10], where these preorders are redened and a denotational characterization for maytesting and musttesting is presented. In [=-=14]-=- a probabilistic extension of CSP (PCSP) that maintains nondeterminism is introduced. The model is provided with an operational semantics, and several denotational semantics are given, based on differ... |

21 | Acceptance trees for probabilistic processes.
- Núñez, Frutos, et al.
- 1995
(Show Context)
Citation Context ...ntroduced; this topic is also studied in [4]. In [11] several equivalences between processes are presented. Based on CSP, we can cite [5, 6], where a reactive interpretation is considered, whereas in =-=[16]-=- a generative one is presented. In both models fully abstract testing semantics with respect to denotational semantics, which are based on acceptance trees, are presented. Nevertheless, the main idea ... |

18 |
Testing Equivalences for Probabilistic Processes
- Christoff
- 1990
(Show Context)
Citation Context ...terministic processes. The alternating of both kinds of processes is necessary, this is why the model is called alternatingsmodel. Besides the models already mentioned, several languages based on CCS =-=[4, 11, 13]-=- that analyze several semantic aspects have been proposed. Thus, in [13] a notion of bisimulation between probabilistic transition systems is introduced; this topic is also studied in [4]. In [11] sev... |

16 |
A remark on bisimulation between probabilistic processes
- Bloom, Meyer
- 1989
(Show Context)
Citation Context ..., several extensions to classical process algebra models have been proposed including time, priorities and probabilities. One of the rst papers describing processes with a probabilistic behaviour is [=-=2-=-], where the concept of probabilistic experiments is introduced. In [7] PCCS is dened as an algebraic language based on the synchronous version of CCS where the nondeterministic choice is replaced by ... |

8 |
A sound and complete proof system for probabilistic processes
- Cuartero, Frutos, et al.
- 1997
(Show Context)
Citation Context ...tion of bisimulation between probabilistic transition systems is introduced; this topic is also studied in [4]. In [11] several equivalences between processes are presented. Based on CSP, we can cite =-=[5, 6]-=-, where a reactive interpretation is considered, whereas in [16] a generative one is presented. In both models fully abstract testing semantics with respect to denotational semantics, which are based ... |

6 |
PCSP: A denotational model for probabilistic processes
- Cuartero, Frutos, et al.
- 1996
(Show Context)
Citation Context ...tion of bisimulation between probabilistic transition systems is introduced; this topic is also studied in [4]. In [11] several equivalences between processes are presented. Based on CSP, we can cite =-=[5, 6]-=-, where a reactive interpretation is considered, whereas in [16] a generative one is presented. In both models fully abstract testing semantics with respect to denotational semantics, which are based ... |

4 | Re nement-oriented probability for CSP - Morgan, McIver, et al. - 1994 |

4 |
Reactive, generative ans strati models of probabilistic processes
- Glabbeek, Smolka, et al.
- 1995
(Show Context)
Citation Context ... language based on the synchronous version of CCS where the nondeterministic choice is replaced by a probabilistic choice: P [p i ]E i , where p i is the probability the process behaves like E i . In =-=[17-=-], this model is extended and This work has been partially supported by the CICYT project Formal development of distributed systems, TIC97-0669-c03-02. three interpretations for concurrent probabilis... |

3 |
TPAL: A timedprobabilistic model for concurrent processes
- Bueno, Valero, et al.
- 1997
(Show Context)
Citation Context ...are given, based on different kinds of observations (trace, broom and barb semantics), where semantic objects are trees with three kinds of nodes: probabilistic, nondeterministic and action nodes. In =-=[3]-=- TPAL is introduced, an algebraic language with time and probabilities, based on LOTOS, where internal choice is replaced by a probabilistic choice. Alternation of both probabilistic and nondeterminis... |

3 | Reactive, generative ans stratified models of probabilistic processes - Glabbeek, Smolka, et al. - 1990 |