On the problem of masking special errors by signature analyzers 1

Signature analysis is an important compact method in digital testing. Applying this method, a test response sequence of a device under test is compressed by a linear feedback shift register (LFSR, for short). Masking occurs if a faulty device yields the same signature as the corresponding good device. Due to the linearity of any LFSR, this happens if and only if the 'error sequence' which is obtained by the 'exor' operation from the correct and the incorrect sequence, leads to the zero signature. The masking properties of signature analyzers depend widely on their structure which can be expressed algebraically by properties of their 'characteristic polynomials'. There are three main directions of research in masking properties of signature analyzers: (i) more general masking results either expressed by the characteristic polynomial or in terms of other LFSR properties; (ii) 'quantitative' results, mostly expressed by computations or estimations of error probabilities; (iii) 'qualitative' results, e.g. concerning the general possibility or impossibility of LFSR to mask special types of error sequences. Following the third direction, we present a survey of masking properties of signature analyzers concerning error sequences having any odd weight, in the lecture. There are some results but also many open problems in this field. We have found some further insights in these problems by computer simulations.