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Linear finite-state machines (LFSMs) such as linear feedback shift registers (LFSRs), cellular automata (CA), and ring generators (RGs) are used as test pattern generators in built-in self-test schemes that employ 2-D scan design. These mechanisms are usually accompanied by phase shifters (PSs) in order to avoid the degradation of the fault coverage caused by correlations/dependences in the produced test bit sequences. Given this context, we investigate in this paper the potential of generalized (or Galois) LFSRs (GLFSRs) as onboard test pattern generators. We compare GLFSRs with and without PSs against LFSMs with PSs (LFSM/PSs) for various types of LFSMs (LFSRs, CA, RGs, and dense RGs) on two accounts: channel separation and overall hardware cost. Experimental results show that GLFSRs achieve larger channel separation with lower hardware cost than LFSM/PS and attain higher fault coverage.