A new built-in TPG method for circuits with random patternresistant faults

859 which means that x a , x a , x a are linearly independent mod ~ P (x) as specified by Lemma 1.1 in the form given by [13], since in the LFSR/SR structure the zeroth cell of the LFSR part is indexed with 0. 2) General LFSM and groups of cells with indexes greater than d 01. In this case set A = fa 1 ; a 2 ;. .. ; a k g is such that a i d, 1 i k, that is, no cell lies within the LFSM part of the LFSM/SR. This case is important in TPG since the SR part of an LFSM/SR is many times a scan chain which is responsible for providing all test-phase inputs (primary outputs and internal flip–flops, plus any additional internal test input points) with test values, while the LFSM part is responsible for providing with values only the SR part (and not directly any proper circuit inputs). Then all () values are the same with (a i) = d 0 1, and so all D x sets are also the same with D (a) = D d01. The () values are (ai) = amax 0 ai = a1 0 ai. So the formula now becomes a 2A j2D x d010j+(a) = (x (a) + x (a) +1 11+x (a)) j2D x d010j = (x a 0a +x a 0a + 111+x a 0a) j2D x d010j = 0 mod P (x): But since the second term in the above product is of degree less than d and P (x) is an irreducible polynomial, P (x) must divide the first term x a 0a + x a 0a + 11 1+x a 0a. But as shown in the case above, this is equivalent to x a 0a +1 11+x a 0a +x a 0a + 111+x a 0a being divisible by ~ P (x), which is the condition of Lemma 1.1. That is, in this case, all LFSMs with the same characteristic polynomial P (x) have the same behavior as a Type-1 LFSR with characteristic polynomial P (x) (as expected, since every cell j after the (d 0 1)th receives just a shift-by-j version of the characteristic sequence of the LFSM). IV. CONCLUSION We investigated the linear dependencies in an LFSM/SR TPG for an arbitrary LFSM. We obtained a formula that relates the linear dependencies with the characteristic …