A Linear Feedback Shift Register (LFSR)can be used to compress test response data as a SignatureAnalyzer(SA). Parallel Signature Analyzers (PSAs) implemented as multiple input LFSRs are faster and re-quire less hardware overhead than Serial Signature Analyzers (SSAs)for compacting test response data forBuilt-In Serf-Test (BIST)in IC or hoard-testing environments. However, the SAs are prone to aliasing errorsbecause of some specific types of error patterns. An alias is a faulty output signature that is identical to thefault-free signature. A penetrating analysis of detecting capability of SAs depends strongly on mathematicalmanipulations, instead of being aware of some special cases or examples. In addition , the analysis should notbe restricted to a particular structure of LFSR, but be appropriate for various structures of LFSRs. This pa-per presents necessary and sufficient conditions for aliasing errors based on a complete mathematical descrip-tion of various types of SAs. An LFSR reconfiguration scheme is suggested which will prevent any aliasingdouble errors. Such a prevention cannot be obtained by any extension of an LFSR. A Linear Feedback Shift Register (LFSR) can be used to compress test response data as a Signature Analyzer (SA). Parallel Signature Analyzers (PSAs) implemented as multiple input LFSRs are faster and re-quire less hardware overhead than Serial Signature Analyzers (SSAs) for compacting test response data for built-in test (BIST) in IC or hoard-testing environments. However, the SAs are prone to aliasing errorsbecause of some specific types of error patterns. An alias is a faulty output signature that is identical to Thefault-free signature. A penetrating analysis of detecting capability of SAs depends strongly on mathematicalmanipulations, instead of being aware of some special cases or examples. In addition, the analysis should notbe restricted to a particular structure of LFSR, but be appropriate for various structures of LFSRs. This pa-per presents necessary and sufficient conditions for aliasing errors based on a complete mathematical descrip tion of various types of SAs. An LFSR re configuration scheme is suggested which will prevent any aliasing double errors. Such a prevention can not be obtained by any extension of an LFSR.