Bounds on signature analysis aliasing for random testing

Abstract

Simple bounds on the aliasing probability for serial signature analysis are presented. To motivate the study, it is shown that calculation of exact aliasing is NP-hard and that coding theory does not necessarily help. It is shown that the aliasing probability is bounded above by 2/(L+2) for test lengths L less than the period, L/sub c/, of the signature polynomials; for test lengths L that are multiples of L/sub c/, the aliasing probability is bounded above by 1; and, 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 automata).<>