Limitations of hybrid systems

Abstract. We examine the ability of combining symbolic and subsym-bolic approaches b y means of recursively encoding and decoding struc-tured data. We show that encoding of symbolic data is possible in this w ay { hence neural netw orks seem well suited for control or classication in symbolic approaches { whereas decoding requires an increasing com-plexit y of the decoding function { hence netw orks with this dynamics are not adequate for producing structured data. Real labeled tree structures reject a smooth encoding in general. 1.