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The design of space-efficient support hardware for built-in self-testing (BIST) is of immense significance in the synthesis of present day very large-scale integration (VLSI) circuits and systems, particularly in the context of design paradigm shift from system-on-board to system-on-chip (SOC). This paper presents an overview of the general problem of designing zero-aliasing or aliasing-free space compression hardware in relation to embedded cores-based SOC for single stuck-line faults in particular, extending the well-known concepts of conventional switching theory, and of incompatibility relation to generate maximal compatibility classes (MCCs) utilizing graph theory concepts, based on optimal generalized sequence mergeability, as developed by the authors in earlier works. The paper briefly presents the mathematical basis of selection criteria for merger of an optimal number of outputs of the module under test (MUT) for realizing maximum compaction ratio in the design, along with extensive simulation results on International Symposium on Circuits and Systems or ISCAS 85 combinational and ISCAS 89 full-scan sequential benchmark circuits, with simulation programs ATALANTA, FSIM, and COMPACTEST.