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A synchronous sequential machine realizable in the form of a loop-free circuit of trigger flip-flops and combinational gates is called a trigger machine. This paper studies the properties of this class of machines. Most importantly, canonical circuit forms and canonical algebraic representations are presented. Other basic properties of trigger machines, many of which closely parallel those of definite machines, are also presented. It is shown that the class of trigger machines forms a Boolean algebra and that, unlike definite machines, they are closed under reversal.