A sequential machine is “consistent” iff when both the input and output strings of symbols are regarded as representing numerical quantities according to conventional interpretations (quantitatively more significant symbols occurring earlier than less), then the machine may be regarded as calculating an ordinary numerical function for all possible input strings. Consistent sequential machines have not been of significant interest to automata theorists but they may have applications in signal processing. The relationships holding among (i) input—output alphabets and (ii) structures of consistent sequential machines and (iii) properties of numerical functions thus realized, are explored. In connection with (ii), the finite state and permutation-free properties are of particular interest. In connection with (iii), the properties of monotonicity, invertibility, piecewise linearity, and differentiability, are of particular interest. Synthesis methods are not significantly treated.
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