A deterministic test-pattern-generation algorithm for synchronous sequential circuits is presented. The algorithm, called Essential, takes advantage of a procedure for learning global implications. It uses static and dynamic dominance relationships among signals, the concept of the potential propagation path, and intelligent heuristics to guide and accelerate the decision-making process for deterministic automatic test pattern generation (ATPG). Essential is based on the well-known method of reverse time processing, but it applies forward processing within time frames to avoid disadvantageous a priori determination of a path to be sensitized or of a primary output to which the fault effects must be propagated. It is designed to exploit fully the sophisticated techniques used for combinational circuits in the Socrates ATPG system. Experimental results for sequential ATPG obtained with Essential (implemented in C on a Sequent Symmetry computer) are reported.