Definition 1.2.1: A deterministic transition system (DTS) is a triple, T = (S, _, _), where S, the states, and _, the input alphabet, are finite non-empty sets, and _ is a function, _ : S _______S, the next-state function.
Definition 1.2.2: If T = (S, _, _) is a deterministic transition system, then the transition function, _* is the function, _* : S _____*___S, defined inductively for all s__S by: _*(s, _) = s, and for all x____* and ____, _*(s, x_) = _(_*(s, x), _).
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