On properties of algebraic transformation and the multifault testability of multilevel logic

The authors present a number of results exploring the relationship between algebraic transformations for area optimization and the testability of combinational logic circuits. They show that for each multifault in an algebraically factored circuit there is an equivalent multifault in the original circuit, and it is well known that two-level single-output circuits that are single-fault testable are also multifault testable. They also show how these results imply that algebraic factorization may be applied to minimized (and therefore completely single-fault testable) two-level circuits, in order to synthesize area optimized, completely multifault testable circuits. Furthermore, when algebraic factorization is applied to a minimized two-level circuit all tests needed for complete multifault coverage of the synthesized circuit can be derived from the single-fault tests for the original two-level circuit.<>