Definition 3.1.1: A deterministic generalized sequential machine (DGSM) M is a 6-tuple, M = (S, _, _, _, _, s0), where (S, _, _) is a deterministic transition system, _ is a finite non-empty set (the output alphabet), s0__S (the start state), and _: S_______* (the output function).
We also extend _ to the closely related function _*: S____*____* operating on sequences of inputs with the inductive definition (for all s__S): __*(s, _) = _, _*(s, x_) = _*(s, x) _(_(s, x), _) for all x___* and_____.
We regard M as defining a function, M: _* ___*, namely M(x) = _*(s0, x), and we refer to such functions as DGSM functions.
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