Test vector embedding into accumulator-generated sequences: a linear-time solution

The test set embedding problem is typically formed as follows: Given an n-stage pattern-generator and a test set, calculate the minimum number of steps that the generator needs to operate in order to generate all vectors in the test set. The cornerstone of a test set embedding technique is its embedding algorithm. An embedding algorithm, given an n-stage pattern generator initialized to a starting value and an n-bit target vector V, calculates the location of V in the generated sequence. In this paper, a novel algorithm is presented that calculates the location of a vector into a sequence generated by an n-stage accumulator accumulating a constant pattern. The time complexity of the algorithm is of the order O(n). To the best of our knowledge, this is the first embedding algorithm of the order O(n) that has been presented in the literature. Experiments performed on well-known benchmark circuits reveal that complete test sets are embedded in sequences of practically acceptable length.