Probabilistic event structures and domains
Daniele Varacca,Hagen Völzer,Glynn Winskel +2 more
- Vol. 358, Iss: 2, pp 173-199
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TLDR
A key result of this paper is a representation theorem showing how continuous valuations on the domain of a confusion-free event structure correspond to the probabilistic event structures it supports.Abstract:
This paper studies how to adjoin probability to event structures, leading to the model of probabilistic event structures. In their simplest form, probabilistic choice is localised to cells, where conflict arises; in which case probabilistic independence coincides with causal independence. An event structure is associated with a domain--that of its configurations ordered by inclusion. In domain theory, probabilistic processes are denoted by continuous valuations on a domain. A key result of this paper is a representation theorem showing how continuous valuations on the domain of a confusion-free event structure correspond to the probabilistic event structures it supports. We explore how to extend probability to event structures which are not confusion-free via two notions of probabilistic runs of a general event structure. Finally, we show how probabilistic correlation and probabilistic event structures with confusion can arise from event structures which are originally confusion-free by using morphisms to rename and hide events.read more
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Probabilistic event structures and domains
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References
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Domain theory
Samson Abramsky,Achim Jung +1 more
TL;DR: In this paper, the authors define abstract bases as the bases of compact elements of algebraic domains and define the notion of ideal completion as the relation with which a basis can be equipped.
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Petri nets, event structures and domains, part I
TL;DR: To connect the abstract ideas of events and domains of information, it is shown how casual nets induce certain kinds of domains where the information points are certain sets of events, which allows translations between the languages of net theory and domain theory.