On properties of algebraic transformations and the synthesis of multifault-irredundant circuits

The authors explore the relationship between algebraic transformations for area optimization and the testability of combinational logic circuits. It is shown that for each multifault in an algebraically factored circuit there is an equivalent multifault in the original circuit. Using this result, it is shown how algebraic factorization may be applied to minimized two-level circuits, to synthesize area-optimized, completely multifault testable multilevel circuits. When a circuit is synthesized using algebraic factorization from a minimized two-level circuit, a reasonably small set of tests that give complete multifault coverage of the synthesized circuit can be derived from the single-fault tests for the original two-level circuit. It is shown that single-fault testability is not an invariant maintained by algebraic transformations, and a simple single-fault irredundant circuit on which the application of algebraic transformations activate a latent multifault, making the resulting algebraically transformed circuit single-fault redundant is presented