Test Primitives: The Unified Notation for Characterizing March Test Sequences

March algorithms are essential for detecting functional memory faults, characterized by their linear complexity and adaptability to emerging technologies. However, the increasing complexity of fault types presents significant challenges to existing fault detection models regarding analytical efficiency and adaptability. This article introduces the test primitive (TP), a unified notation that characterizes March test sequences through a novel methodology that decouples fault detection operations from sensitization states. The proposed TP achieves platform independence and seamless integration of fault models, supported by rigorous theoretical proofs. These proofs establish the fundamental properties of the TP in terms of completeness, uniqueness, and conciseness, providing a theoretical foundation that ensures the decoupling method reduces the computational complexity of March algorithm analysis to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$O(1)$</tex-math> </inline-formula>. This reduction is analogous to Karnaugh map simplification in digital logic while enabling millisecond-level automated analysis. Experimental results demonstrate that the proposed method significantly enhances both analyzable fault coverage (FC) and detection accuracy, thereby addressing critical limitations of existing fault detection models.