A Primal-Dual Solution to Minimal Test Generation Problem

This newly proposed solution to the minimal test generation problem of combinational circuits is based on (1) identifying independent faults, (2) generating tests for them, and (3) minimizing the tests. The third part, test minimization, is accomplished by an already known solution using integer linear programming (ILP). Using the theory of primal-dual linear programs, we model the independent fault set identification as the dual of the test minimization problem. A solution of the dual problem, whose existence is guaranteed by the duality theorem, gives us a conditionally independent fault set (CIFS). We start with any (non-optimal but complete) vector set. Our CIFS is, therefore, not absolute but is specific to the starting vector set. Successively adding more vectors for the identified independent set and solving the dual problem, we bring the independent set closer to its minimal size. Finally, a primal solution minimizes the set of all accumulated vectors. Benchmark results show potential for both smaller test sets and lower CPU times.