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Simple Bounds on Serial Signature Analysis Aliasing for Random Testing
May 1992 (vol. 41 no. 5)
pp. 638-645

It is shown that the aliasing probability is bounded above by (1+ epsilon )/L approximately=1/L ( epsilon small for large L) for test lengths L less than the period, L/sub c/, of the signature polynomial; for test lengths L that are multiples of L/sub c/, the aliasing probability is bounded above by 1; for test lengths L greater than L/sub c/ and not a multiple of L/sub c/, the aliasing probability is bounded above by 2/(L/sub c/+1). These simple bounds avoid any exponential complexity associated with the exact computation of the aliasing probability. Simple bounds also apply to signature analysis based on any linear finite state machine (including linear cellular automaton). From these simple bounds it follows that the aliasing probability in a signature analysis design using beta intermediate signatures is bounded by ((1+ epsilon )/sup beta / beta /sup beta /)/L/sup beta /, for beta >L and L/ beta >L/sub c/. By using intermediate signatures the aliasing probability can be substantially reduced.

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Index Terms:
serial signature analysis aliasing; random testing; aliasing probability; signature polynomial; simple bounds; linear finite state machine; linear cellular automaton; intermediate signatures; computational complexity; finite automata; integrated circuit testing; logic testing; probability.
N.R. Saxena, P. Franco, E.J. McCluskey, "Simple Bounds on Serial Signature Analysis Aliasing for Random Testing," IEEE Transactions on Computers, vol. 41, no. 5, pp. 638-645, May 1992, doi:10.1109/12.142690
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