REPORT Mayo98a/IDIAP On the Complexity of Recognizing Regions Computable by Two-Layered Perceptrons Mayoraz, Eddy EXTERNAL http://publications.idiap.ch/attachments/reports/1998/rr98-03.pdf PUBLIC Idiap-RR-03-1998 1998 IDIAP This work is concerned with the computational complexity of the recognition of $ÞPtwo$, the class of regions of the Euclidian space that can be classified exactly by a two-layered perceptron. Some subclasses of $ÞPtwo$ of particular interest are also studied, such as the class of iterated differences of polyhedra, or the class of regions $V$ that can be classified by a two-layered perceptron with as only hidden units the ones associated to $(d-1)$-dimensional facets of $V$. In this paper, we show that the recognition problem for $ÞPtwo$ as well as most other subclasses considered here is \NPH\ in the most general case. We then identify special cases that admit polynomial time algorithms.