Iterative Exhaustive Pattern Generation for Logic Testing

Abstract

Exhaustive pattern logic testing schemes provide all possible input patterns with respect to an output in the set of test patterns. This paper is concerned with the problem that arises when this is to be done simultaneously with respect to a number of outputs, using a single test set. More specifically, in this paper we describe an iterative procedure for generating a test set consisting of n-dimensional vectors which exhaustively covers all k-subspaces simultaneously, i.e., the projections of n-dimensional vectors in the test set onto any input subset of a specified size k contain all possible patterns of k-tuples. For any given k, we first find an appropriate N (N>k) and generate an efficient N-dimensional test set for exhaustive coverage of all k-subspaces. We next develop a constructive procedure to expand the corresponding test matrix (formed by taking test vectors as its rows) such that a test set of N <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> -dimensional vectors exhaustively covering the same k-subspaces is obtained. This procedure may be repeated to cover arbitrarily large n (equation after i iterations), while keeping the same k. It is shown that the size of the test set obtained this way grows in size which becomes proportional to (log n) raised to the power of [log (q+1)], where q is a function of k only, and is approximated (bounded closely below) by k <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> /4 in binary cases. This approach applies to nonbinary cases as well except that the value of q in an r-ary case is approximated by a number lying between k <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> /4 and k <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> /2.