Exact Classification with Two-Layered Perceptrons

We study the capabilities of two-layered perceptrons for classifying exactly a given subset. Both necessary and sufficient conditions are derived for subsets to be exactly classifiable with two-layered perceptrons that use the hard-limiting response function. The necessary conditions can be viewed as generalizations of the linear-separability condition of one-layered perceptrons and confirm the conjecture that the capabilities of two-layered perceptrons are more limited than those of three-layered perceptrons. The sufficient conditions show that the capabilities of two-layered perceptrons extend beyond the exact classification of convex subsets. Furthermore, we present an algorithmic approach to the problem of verifying the sufficiency condition for a given subset

The Compensation Approach for Three or More Dimensional Random Walks

In this paper we investigate for which random walks with three or more dimensions the compensation approach can be used to determine the equilibrium distribution. As we will see, the compensation approach is not appropriate for the symmetric shortest queue system with three queues, but for the 2 x 3 buffered switch it is. By using this compensation approach, we show that for the 2 x 3 buffered switch the equilibrium distribution can be expressed as a linear combination of six series of binary trees of product-form (geometric) distributions

On-line lot-sizing with perceptrons

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