Determining Aliasing Probabilities in BIST by Counting Strings

The aliasing probability (AP) of a Built-In Self-Test (BIST)architecture is the probability that an error response gets classified as agood response. A general technique to determine the AP for many common andalternative BIST response analysis (RA) architectures is presented here.This technique models the RA circuit as a Deterministic Finite Automaton(DFA), and determines the AP by counting the ratio of strings accepted bythe DFA to the total number of possible error strings. The strings acceptedby a DFA can be calculated by counting the paths in the DFAs statetransition graph (STG). Moreover, if the STG is complete, then theAP(k) = ((1/N)N^k-1)/(N^k-1), where k is the testlength and N is the number of states and input symbols. Thistechnique is demonstrated by determining the APs for the following RAarchitectures: Multiple-Input Shift Registers (MISRs), Cellular Automata(CA), Linear Feedback Shift Registers (LFSRs), accumulators, and a set ofalternative architectures directly based on DFAs. This paper also shows howthe adjacency matrix of the STG can be used to directly determine the AP ofany RA architecture modeled as a DFA. Finally, the eigenvalues andeigenvectors of the DFAs STG adjacency matrix are used to derive generalexpressions for the DFAs AP.