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A new technique of synthesizing totally symmetric Boolean functions is presented that achieves complete robust path-delay fault testability. We show that every consecutive symmetric function can be expressed as a logical composition (e.g., AND, NOR) of two unate symmetric functions, and the resulting composite circuit can be made robustly path-delay fault testable, if the constituent unate functions are synthesized as two-level irredundant circuits. Nonconsecutive symmetric functions can also be synthesized by decomposing them into a set of consecutive symmetric functions. The circuit cost of the proposed design can further be reduced by a novel algebraic factorization technique based on some combinatorial clues. The overall synthesis guarantees complete robust path-delay fault testability, and can be completed in linear time. The results shows that the proposed method ensures a significant reduction in …