## On the Operational Semantics of Nondeterminism and Divergence (1995)

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Citations: | 2 - 0 self |

### BibTeX

@MISC{Erdogmus95onthe,

author = {Hakan Erdogmus and Robert Johnston and Michael Ferguson},

title = {On the Operational Semantics of Nondeterminism and Divergence},

year = {1995}

}

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### Abstract

An operational model of nondeterministic processes coupled with a novel theory of divergence is presented. The operational model represents internal nondeterminism without using explicit internal transitions. Here the notion of internal state e#ectively replaces the familiar notion of internal transition, giving rise to an alternative operational view of processes: the weak process. Roughly, a weak process is a collection of stable internal states together with a set of transitions each of which is defined from an internal state to another weak process. Internal nondeterminism arises from such refinement of processes into multiple internal states. A simple extension to the basic weak process model gives rise to an elaborate operational theory of divergence. According to this theory, the ability of a process to undertake an infinite internal computation which is pathological, or persistent, is distinguished from its ability to undertake an infinite internal computation which is not. Alt...

### Citations

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Citation Context ... ultimate effect on the external behavior of a system in which they occur may be detectable. Another class of process algebras capture directly this effect: internal nondeterminism. Examples are TCSP =-=[5], the ��-=-�� -less version of CCS proposed in [9], and the process algebra described in [14]. All of these languages --- in place of a �� -like construct --- supply an internal choice construct. This in t... |

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Citation Context ...here are numerous behavioral equivalences defined on the structure of an LTS. Examples can be found in [8], [7], [19], and [18]. Perhaps the most well-known of all is Milner's observation equivalence =-=[21]-=-. The original definition of observation equivalence was inductive. Later, it was given a more workable formulation based on Park's notion of bisimulation [24]. Park's formulation had an impact on the... |

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Citation Context ...otion of bisimulation [24]. Park's formulation had an impact on the way behavioral relations were defined: several other researchers that followed used similar formulations in a variety of frameworks =-=[18, 29, 10]-=-. Although most existing denotational theories of concurrency do not require an explicit notion of internal action, or transition, for a satisfactory treatment of nondeterminism, the literature lacks ... |

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Citation Context ...semantics to the likes of LOTOS's problematic hiding construct [19] is particularly interesting. 1.1 Background and Motivation Several process algebraic languages such as CCS [20], ACP [3], and LOTOS =-=[27]-=-, provide a special prefix construct to express the notion of internal computation, or transition. It is assumed that the environment can neither control the undertaking of such computations nor obser... |

33 |
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Citation Context ...ct or induced indirectly by a preorder (transitive and reflexive relation). There are numerous behavioral equivalences defined on the structure of an LTS. Examples can be found in [8], [7], [19], and =-=[18]-=-. Perhaps the most well-known of all is Milner's observation equivalence [21]. The original definition of observation equivalence was inductive. Later, it was given a more workable formulation based o... |

22 |
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Citation Context ...rgence which is more elaborate than the ones found in the literature. The application of the extended ATS model in assigning operational semantics to the likes of LOTOS's problematic hiding construct =-=[19]-=- is particularly interesting. 1.1 Background and Motivation Several process algebraic languages such as CCS [20], ACP [3], and LOTOS [27], provide a special prefix construct to express the notion of i... |

19 |
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Citation Context ...a system in which they occur may be detectable. Another class of process algebras capture directly this effect: internal nondeterminism. Examples are TCSP [5], the �� -less version of CCS proposed=-= in [9], an-=-d the process algebra described in [14]. All of these languages --- in place of a �� -like construct --- supply an internal choice construct. This in turn gives rise to a more abstract and cleaner... |

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Citation Context ...icipants offer that action at the same instant. This regime of process interaction is often referred to as synchronous communication (also known as rendez-vous). As do many other models and languages =-=[16, 20, 5, 3, 11, 14, 27]-=-, we combine synchronous communication with asynchronous evolution, i.e, assume that communicating processes evolve at independent speeds. 2.3 Concurrency and Nondeterminism Let P be a process which o... |

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Citation Context ...particular interpretation adopted, and the suggested semantics of the hiding construct can easily be modified to conform to interpretation (I). 2 It should be pointed out that observation equivalence =-=[21, 1]-=-, testing equivalence [4, 19], failure equivalence [6] and must-testing equivalence [8, 14] are all based upon a form of external testing which is compatible with interpretation (I) rather than with i... |

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Citation Context ...reactive system. As such, the LTS model supplies a common basis for studying the interrelations between several existing operational theories of concurrency and nondeterminism (for examples, see [7], =-=[12]-=-, and [19]). In particular, it has been adopted as the underlying operational model for CCS and LOTOS. In the heart of a LTS is a transition relation defined on a set of processes. The transition rela... |

2 | eds.. CONCUR ’90, Theories of Concurrency: Unification and Extension - Baeten, Klop |

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