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Ali Jalal-Kamali, The University of Texas at El PasoFollow Ondrej Nebesky, The University of Texas at El PasoFollow Michael H. Durcholz, The University of Texas at El PasoFollow Vladik Kreinovich, The University of Texas at El PasoFollow Luc Longpre, The University of Texas at El PasoFollow
6-2011
Technical Report: UTEP-CS-11-32
To appear in Journal of Uncertain Systems, 2012, Vol. 6, No. 2.
In many application areas, it is important to study "generic" properties, i.e., properties which hold for ``typical'' examples. For example, if we know the probabilities of different events, we can consider a "random" object -- i.e., an object that, crudely speaking, does not belong to any class of "unusual" events (i.e., to any class with a small probability). In other cases, "typical" may mean not belonging to an "unusual" subset which is small in some other sense -- e.g., a subset of a smaller dimension. The corresponding notion of "typicalness" has been formalized for several cases, including the case of random events. In this case, the known Kolmogorov-Martin-Lof definition of randomness captures the idea that properties with probability 0 are impossible. In our previous papers, we modified this definition to take into account that from a practical viewpoint, properties with very small probabilities are often considered impossible as well. In this paper, we extend this definition to a general notion of "generic".
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Technical Report: UTEP-CS-11-32
To appear in Journal of Uncertain Systems, 2012, Vol. 6, No. 2.