Random Event Structures
Received:July 04, 2008  Revised:July 28, 2008  Download PDF
Manfred Droste,Guo-Qiang Zhang. Random Event Structures. International Journal of Software and Informatics, 2008,2(1):77~88
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Manfred Droste  Guo-Qiang Zhang
Fund:Preprint sbumitted to Elseiver
Abstract:In a line of recent development, probabilistic constructions of universal, homogeneous objects have been provided in various categories of ordered structures, such as causal sets[12], bifinite domains[13], and countable partial orders[10]. These constructions have been shown to produce objects with the desired properties with probability 1 in an appropriately defined measure space. A common strategy for these constructions is successive point-wise extension of an existing finite structure, with decisions on the relationships between the newly added point and the existing structure made according to well-specified probabilistic choices. This strategy is a departure from (and understandably so due to the increased complexity) the original one for random graphs[16] where a universal homogeneous countable graph is constructed with probability 1 in a single step (i.e., a single round of countably many probabilistic choices made independently). It would be interesting to see which of the categories studied more recently may admit such "one-step" constructions. The main focus of this paper is a new strategy, consisting of a single round of countably many probabilistic choices made independently, for the construction of a universal, homogeneous prime event structure. The intuition that the one-round construction is desirable has a similar flavor to a more general setting in e.g. Calculus/Real Analysis. When taking limits, iterative step by-step processes are usually given, but a set of machineries was invented to determine the limit, i.e., achieving a "one-round" direct and explicit description of the limit.
keywords:event structure  universal domain  randomness  probability and order
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