Summary: Concurrency, -Algebras,
and Probabilistic Fairness
Samy Abbes and Albert Benveniste
PPS/Universit´e Paris 7 Denis Diderot. 175, rue du Chevaleret, 75013 Paris, France
INRIA/IRISA, Campus de Beaulieu, 35042 Rennes Cedex, France
Abstract. We extend previous constructions of probabilities for a prime
event structure E by allowing arbitrary confusion. Our study builds on
results related to fairness in event structures that are of interest per se.
Executions of E are captured by the set of maximal configurations.
We show that the information collected by observing only fair executions
of E is confined in some -algebra F0, contained in the Borel -algebra F
of . Equality F0 = F holds when confusion is finite (formally, for the
class of locally finite event structures), but inclusion F0 F is strict in
general. We show the existence of an increasing chain F0 F1 F2 . . .