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An R-functions based classification approach along with a regularization framework is proposed. The abnormal software process detection problem was used as the test bed. The R-functions based classification method is termed as the R-cloud method. The approach was validated both on synthetic and real-world data. Regularization allows to achieve good generalization and classification performance. In addition, the R-cloud approach gives the benefit of the analytical representation of the decision boundary. The introductory study on practical use of the R-cloud classifiers yielded promising results. The prototyping has shown that application of the R-functions based pattern recognition technique is a significant and practical tool for fault detection in providing fault tolerant computing. [ABSTRACT FROM AUTHOR]