Bojan Hvala, Sandi Klavzar, Franc Novak.
On Y-compatible and strict Y-compatible functions,
Applied Mathematics Letters, Vol. 10, No. 1, pp. 79-82, 1997.

This work was initiated by the problems of storage and processing of measured response data of analog circuits normally used by the fault dictionary techniques in fault localization. We explore the possibility of data compression of a series of real numbers representing given response data. In particular, we are looking for some data compression function that would enable us to determine for any two given responses y1,y2,...,yn and z1,z2,...,zn whether zi (is equal or smaller than) yn holds for all i merely on the basis of their compressed data (i.e., signatures). If such data compression function existed, regions that characterize the response of a circuit could be simply described by the signatures of their margins. Besides, it would also be possible to determine from the signature of the response if the operation of a circuit-under-test lies in the given region or not. The notion of Y-compatible function is introduced that can be used for the definition of ranges that characterize the response of a circuit by the compressed data of their margins. The proof of nonexistence of Y-compatible polynomial function is presented. The proof indicates the limits in data compression of analog signatures.