Finite States and Finite Automata

In the States classification ( and also in  Halting or not-Halting) the class of programs with finite states seem very close to the finite automata definition in both cases the program has a finite number of states but the central difference is that in the first case the limits come directly from the construction and in the second there is not a limit by construction , the program can be in one of the 2 class and it is also uncomputable to recognize at which class a program belongs.

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