One-layer perceptrons can’t compute certain functions
E.g. they can't compute: Parity—whether an odd or even no. of units in the input layer are active—and Connectedness—whether all active units in the input layer are connected to all other active units, either directly, or via other active units.
Martin Minsky & Seymour Papert (1969), as articulated by David Rumelhart, James McClelland, and FARG (1986b).