Trust in global computing systems as a limit property emerging from short range random interactions 125 Effie Makri University of the Aegean, Department of Mathematics Greece AbstractToday we are witnessing a major reconsideration of the computing paradigm, as evidenced by the abundance and increasing frequency of use of novel terms such as ambient intelligence, ubiquitous computing, disappearing computer, grid computer, global computing and mobile ad-hoc networks. Systems that can be described with such terms are of a dynamic, with no clear physical boundary, nature and it seems that it is impossible (or, at least, difficult) to define sharply a number of important properties holding with certainty and throughout the whole lifetime of the system. In this chapter we propose a new paradigm for the concept of trust that can be applicable to describing trust related properties in evolving, "boundary-transcending", computing systems. This paradigm is founded on the interaction between formal logic and threshold phenomena, i.e. properties of large combinatorial structures that can be proved to emerge with certainty, as the system evolves. We define a number of notions of trust within these frameworks and pinpoint their inherent weakness in providing clear and measurable trust properties. We then argue that trust in dynamic, global computing systems must, necessarily, incorporate, to some degree, some non-formalizable elements, such as common sense and intuition in order to overcome formalism's weaknesses and result in a pragmatic notion of trust applicable to today's new computing paradigms.
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