Probabilistic event structures and domains

  • Authors:

  • Daniele Varacca;Hagen Völzer;Glynn Winskel

  • Affiliations:

  • Department of Computing, Imperial College, London, UK and LIENS, École Normale Supérieure, Paris, France;Institut für Theoretische Informatik, Universität zu Lübeck, Germany;Computer Laboratory, University of Cambridge, UK

  • Venue:
  • Theoretical Computer Science - Concurrency theory (CONCUR 2004)
  • Year:
  • 2006

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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.