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By K. Nakamatsu, M. Abe (Editors)

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Vong et al. / Data Transformation in Modern Petrol Engine Tune-up 27 because the input features themselves are highly (and perhaps nonlinearly) correlated. Several preprocessing methods from machine learning, support vector machines (SVM) and statistics are compared to verify their ability to handle the issues of high dimensionality and nonlinear correlation. In the comparison, a testing application of petrol engine tune-up is selected since it involves a moderate number of dimensions (≥ 70) and the engine features are nonlinearly correlated.

In section 2 we give the basic notations. Section 3 presents the definition of the improved recursive decomposition ordering with status (IRDS) and we completely show that IRDS is closed under substitutions. Also, we review that the IRDS is a simplification ordering. 2. Preliminaries We mainly follow the basic notations of [14,19]. An abstract reduction system (ARS for consisting of a set and a binary relation . We say short) is a pair is terminating if there is no infinite sequence of that ARS elements in .

Toyama: An improved recursive decomposition ordering for higher-order rewrite systems, IEICE Transactions on Information and Systems E81-D (9) (1998), 988–996. [7] M. Thesis, JAIST, 1999. [8] J. P. Jouannaud and P. Lescanne and F. Reinig: Recursive decomposition ordering, in: Proc. of Working Conf. II (IFIP), ((GarmischParternkirchen, Germany, 1982), North-Holland Publishing Company, 1983), 331–348. [9] J. P. Jouannaud and A. Rubio: A recursive path ordering for higher-order terms in -long -normal form, in: Proc.

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