On Y-compatible and strict Y-compatible functions,

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.