## A Fully Abstract Metric-Space Denotational Semantics for Reactive Probabilistic Processes (1998)

Venue: | In Proc. COMPROX '98, Electronic Notes in TCS vol.13 |

Citations: | 7 - 1 self |

### BibTeX

@INPROCEEDINGS{Kwiatkowska98afully,

author = {M. Z. Kwiatkowska and G. J. Norman},

title = {A Fully Abstract Metric-Space Denotational Semantics for Reactive Probabilistic Processes},

booktitle = {In Proc. COMPROX '98, Electronic Notes in TCS vol.13},

year = {1998},

publisher = {Elsevier}

}

### OpenURL

### Abstract

Metric-Space Denotational Semantics for Reactive Probabilistic Processes M.Z. Kwiatkowska and G.J. Norman School of Computer Science, University of Birmingham, Edgbaston, Birmingham B15 2TT, UK Abstract We consider the calculus of Communicating Sequential Processes (CSP) [8] extended with action-guarded probabilistic choice and provide it with an operational semantics in terms of a suitable extension of Larsen and Skou's [14] reactive probabilistic transition systems. We show that a testing equivalence which identi es two processes if they pass all tests with the same probability is a congruence for a subcalculus of CSP including external and internal choice and the synchronous parallel. Using the methodology of de Bakker and Zucker [3] introduced for classical process calculi, we derive a metric-space semantic model for the calculus and show it is fully abstract.

### Citations

3409 | Communicating Sequential Processes
- Hoare
(Show Context)
Citation Context ...d Norman tions of two processes are equal precisely when their operational meanings are equivalent. Many probabilistic extensions of process calculi have been proposed to date, based on CCS [17], CSP =-=[5-=-] and ACP [4] and including amongst others [6,7,16,19,23]. Likewise, several probabilistic equivalences have been introduced, for example: probabilistic bisimulation, dened by Larsen and Skou [14] for... |

3218 | Communication and Concurrency - Milner - 1989 |

583 |
The Theory and Practice of Concurrency
- Roscoe
- 1998
(Show Context)
Citation Context ...er than the CSP equivalences of [16,23] but incomparable to that of [19]. 3 The Process Calculus In this section, we present the process calculus for reactive probabilistic processes RP, based on CSP =-=[5,8,2-=-1], in which prexing is replaced with actionguarded probabilistic choice. We begin by introducing the notation necessary to derive our calculus and investigate its properties. Denition 3.1 (Process Ca... |

405 | Bisimulation through probabilistic testing
- Larsen, Skou
- 1991
(Show Context)
Citation Context ...v R F if E v glb F and E v lub F , and E R F if E v R F and F v R E. Thus, the order v R is an intersection of orders v glb and v lub . The equivalence R is coarser than probabilistic bisimulation [1=-=4]-=-, and yet non-probabilistic branching time. It issner than the CSP equivalences of [16,23] but incomparable to that of [19]. 3 The Process Calculus In this section, we present the process calculus for... |

360 | Process algebra for synchronous communication - Bergstra, Klop |

271 | Probabilistic simulations for probabilistic processes
- Segala, Lynch
- 1994
(Show Context)
Citation Context ..., dened by Larsen and Skou [14] for reactive systems and extended with non-determinism by Hansson [7]; probabilistic equivalences of Jou and Smolka [11]; probabilistic simulation of Segala and Lynch [=-=22-=-]; Wang Yi and Larsen's testing equivalence [24]; and CSP equivalences of Morgan et al. [19], Lowe [16] and Seidel [23]. The above equivalences dier in their discriminating power, and also in how they... |

153 | Reactive, generative, and stratified models of probabilistic processes
- Glabbeek, Smolka, et al.
- 1995
(Show Context)
Citation Context ...cisely when their operational meanings are equivalent. Many probabilistic extensions of process calculi have been proposed to date, based on CCS [17], CSP [5] and ACP [4] and including amongst others =-=[6,7,16,19,23]-=-. Likewise, several probabilistic equivalences have been introduced, for example: probabilistic bisimulation, defined by Larsen and Skou [14] for reactive systems and extended with non-determinism by ... |

147 |
Time and probability in formal design of distributed systems
- Hansson
- 1994
(Show Context)
Citation Context ...cisely when their operational meanings are equivalent. Many probabilistic extensions of process calculi have been proposed to date, based on CCS [17], CSP [5] and ACP [4] and including amongst others =-=[6,7,16,19,23-=-]. Likewise, several probabilistic equivalences have been introduced, for example: probabilistic bisimulation, dened by Larsen and Skou [14] for reactive systems and extended with non-determinism by H... |

125 |
A probabilistic powerdomain of evaluations
- Jones, Plotkin
- 1989
(Show Context)
Citation Context ...ore the original external and internal choice remain part of their model. They give denotational semantics to this calculus by applying the probabilistic powerdomain construction of Jones and Plotkin =-=[10]-=- (which is possible over any directed complete partial order) to an extended failures model for CSP. Intuitively, they consider probabilistic processes as probability distributions over the non-probab... |

78 |
J.I.Zucker: Processes and the Denotational Semantics of Concurrency
- Bakker
- 1982
(Show Context)
Citation Context ...ey pass all tests with the same probability is a congruence for a subcalculus of CSP including external and internal choice and the synchronous parallel. Using the methodology of de Bakker and Zucker =-=[3]-=- introduced for classical process calculi, we derive a metric-space semantic model for the calculus and show it is fully abstract. 1 Introduction When specifying concurrent probabilistic systems, for ... |

69 |
Equivalences, congruences, and complete axiomatizations for probabilistic processes
- Jou, Smolka
- 1990
(Show Context)
Citation Context ...introduced, for example: probabilistic bisimulation, dened by Larsen and Skou [14] for reactive systems and extended with non-determinism by Hansson [7]; probabilistic equivalences of Jou and Smolka [=-=11-=-]; probabilistic simulation of Segala and Lynch [22]; Wang Yi and Larsen's testing equivalence [24]; and CSP equivalences of Morgan et al. [19], Lowe [16] and Seidel [23]. The above equivalences dier ... |

68 |
Solving reflexive domain equations in a category of complete metric spaces
- America, Rutten
- 1989
(Show Context)
Citation Context ...istic transition systems which will distinguish two processes only if they can be differentiated by means of experiments. A (discrete) probability distribution on a set D is a function �� : D \Gam=-=ma! [0; 1] such th-=-at P d2D ��(d) = 1. We use ��(D) to denote the set of discrete probability distributions on D. A subset X of the cartesian product A \Theta S of sets A and S is said to satisfy the reactivenes... |

61 | Quantitative analysis and model checking
- Huth, Kwiatkowska
- 1997
(Show Context)
Citation Context ...cesses on to the same denotation. In [13,20] the equivalence considered here is endowed with a logical characterization in terms of the quantitative variant of the Hennessy-Milner Logic introduced in =-=[9]-=-. This completes the work started in [9] by characterizing the equivalence induced by (a variant of) the quantitative HML. Related research concerning probabilistic extensions of CSP includes the work... |

35 | Refinement-Oriented Probability for CSP
- Morgan, McIver, et al.
- 1996
(Show Context)
Citation Context ...cisely when their operational meanings are equivalent. Many probabilistic extensions of process calculi have been proposed to date, based on CCS [17], CSP [5] and ACP [4] and including amongst others =-=[6,7,16,19,23-=-]. Likewise, several probabilistic equivalences have been introduced, for example: probabilistic bisimulation, dened by Larsen and Skou [14] for reactive systems and extended with non-determinism by H... |

26 | Probabilistic and prioritized models of timed CSP
- Lowe
- 1995
(Show Context)
Citation Context ...m the standard CSP is that an internal probabilistic choice operator replaces the internal (non-deterministic) choice operator, and so the model constructed is fully deterministic. Similarly, in Lowe =-=[15]-=- non-deterministic choice is replaced by internal probabilistic choice, and external choice by prioritised choice. The result is a rather complex semantic model in which all forms of choice are probab... |

20 | Representing nondeterministic and probabilistic behaviour in reactive processes
- Lowe
- 1993
(Show Context)
Citation Context ...cisely when their operational meanings are equivalent. Many probabilistic extensions of process calculi have been proposed to date, based on CCS [17], CSP [5] and ACP [4] and including amongst others =-=[6,7,16,19,23-=-]. Likewise, several probabilistic equivalences have been introduced, for example: probabilistic bisimulation, dened by Larsen and Skou [14] for reactive systems and extended with non-determinism by H... |

19 |
Reactive, generative and strati models of probabilistic processes
- Glabbeek, Steen, et al.
- 1990
(Show Context)
Citation Context |

19 | A testing equivalence for reactive probabilistic processes
- Kwiatkowska, Norman
- 1998
(Show Context)
Citation Context ... metric-space denotational semantics based on the constructions of de Bakker and Zucker [3] and show it is fully abstract, in the sense that it maps equivalent processes on to the same denotation. In =-=[13,20]-=- the equivalence considered here is endowed with a logical characterization in terms of the quantitative variant of the Hennessy-Milner Logic introduced in [9]. This completes the work started in [9] ... |

18 | Probabilistic metric semantics for a simple language with recursion
- Kwiatkowska, Norman
- 1996
(Show Context)
Citation Context ...ple internal choice fails to be idempotent. Solutions to these problems have been investigated in [18]. As far as metric-space denotational models are concerned, we should mention the metric model of =-=[12]-=- where a deterministic subcalculus of CCS extended with action-guarded probabilistic choice was considered, and that of Baier and Kwiatkowska [2] for full CCS extended with action-guarded probabilisti... |

9 | Domain equations for probabilistic processes (Extended Abstract
- Baier, Kwiatkowska
- 1997
(Show Context)
Citation Context ...etween the denotations of E n and E n+1 with respect to the metric d V would be 2 (n+1) , and thus hE n i n is Cauchy as required. In contrast, with respect to the classically derived ultra-metric of =-=[2]-=-, the distance between E n and E n+1 would be 1 2 , and so this convergence property would be lost. Unfortunately, the pseudo-metric d V does not give us the Cauchy sequences we would expect to model ... |

8 |
Solving re domain equations in a category of complete metric spaces
- America, Rutten
- 1989
(Show Context)
Citation Context ...probabilistic transition systems which will distinguish two processes only if they can be dierentiated by means of experiments. A (discrete) probability distribution on a set D is a function : D ! [0=-=;-=- 1] such that P d2D (d) = 1. We use (D) to denote the set of discrete probability distributions on D. A subset X of the cartesian product A S of sets A and S is said to satisfy the reactiveness condit... |

6 | Metric Semantics for Reactive Probabilistic Processes
- Norman
(Show Context)
Citation Context ... metric-space denotational semantics based on the constructions of de Bakker and Zucker [3] and show it is fully abstract, in the sense that it maps equivalent processes on to the same denotation. In =-=[13,20]-=- the equivalence considered here is endowed with a logical characterization in terms of the quantitative variant of the Hennessy-Milner Logic introduced in [9]. This completes the work started in [9] ... |

5 | Argument duplication in probabilistic CSP
- Morgan, McIver, et al.
- 1995
(Show Context)
Citation Context ...er, problems with the behaviour of certain 3 Kwiatkowska and Norman operators in their model, for example internal choice fails to be idempotent. Solutions to these problems have been investigated in =-=[18]-=-. As far as metric-space denotational models are concerned, we should mention the metric model of [12] where a deterministic subcalculus of CCS extended with action-guarded probabilistic choice was co... |