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<p><b>Abstract</b>—Many built-in self-testing (BIST) schemes compress the test responses from a <it>k</it>-output circuit to <it>q</it> signature streams, where <it>q</it> << <it>k</it>, a process termed space compaction. The effectiveness of such a compaction method can be measured by its compaction ratio <it>c</it> = <it>k/q</it>. A high compaction ratio can introduce aliasing, which occurs when a faulty test response maps to the fault-free signature. We investigate the problem of designing zero-aliasing space compaction circuits with maximum compaction ratio <it>c</it><sub><it>max</it></sub>. We introduce a graph representation of test responses to study the space compaction process and relate space compactor design to a graph coloring problem. Given a circuit under test, a fault model, and a test set, we determine <it>q</it><sub><it>min</it></sub>, which yields <it>c</it><sub><it>max</it></sub> = <it>k/q</it><sub><it>min</it></sub>. This provides a fundamental bound on the cost of signature-based BIST. We show that <it>q</it><sub><it>min</it></sub>≤ 2 for all the ISCAS 85 benchmark circuits. We develop a systematic design procedure for the synthesis of space compaction circuits and apply it to a number of ISCAS 85 circuits. Finally, we describe multistep compaction, which allows zero aliasing to be achieved with any <it>q</it>, even when <it>q</it><sub><it>min</it></sub> > 1.</p>
Aliasing, built-in self-testing, fault coverage, graph coloring, multistep compaction.

B. T. Murray, J. P. Hayes and K. Chakrabarty, "Optimal Zero-Aliasing Space Compaction of Test Responses," in IEEE Transactions on Computers, vol. 47, no. , pp. 1171-1187, 1998.
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