Trust in Global Computing Systems as a Limit Property Emerging from Short Range Random Interactions

Abstract

Trust has been one of the cornerstones of the success of modern society in building wellorganized groups of people working towards their own wealth as well as that of theirs peers. This traditional notion of trust, however, has two basic characteristics: i) it is based on personal contact, and ii) frequently, it cannot be explained. Today, it is impossible to have personal information about any entity (either human or a machine offering a service) of the huge and ever expanding dynamic computing society, with which we may want to communicate or perform a transaction. Thus, we would like to rely on rules as well as automated deductive procedures as to whether we should trust an entity or not. In this chapter we have reviewed a number of formalisms with respect to their expressive and deductive power when describing large combinatorial structures, where the structure consists of a number of entities as well as trust assertion among them. Initially we attempted to provide a practical and viable definition of trust for dynamically changing computing environments that can be described within the global computing paradigm. Our view is that trust can be reduced to a number of properties that appear as a limiting behavior in systems under certain conditions. These systems are modeled within the formalism of a random graph model according to the context of the target system. Then the properties can be written formally using the first and second order language of graphs. If the properties can be written in the first order language of graphs then one can use the extension statements in order to establish the conditions under which the model displays threshold behavior and, thus, all the properties hold asymptotically with either probability 0 or 1