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**Finite state machines :(**

Okay, i'm having trouble understanding a finite state machine example in my :yuck: book. It's a state table for the machine M = (S, [tex] \ell [/tex], [tex] \wp [/tex], v , [tex] \omega [/tex]) where S = {S0, S1, S2}, [tex] \ell = \omega = [/tex] {0,1}.

Please check out the attachment What i don't understand is the v and [tex] \omega [/tex] column... Why is row S0; S0 in "0" and S1 in "1", and row S2; 0 in "0" and 1 in "1"?

Is this just made up or something? :tongue2:

In my textbook it says that:

v: S X [tex] \ell [/tex] -> S is the next state function

w: S X [tex] \ell [/tex] -> [tex] \wp [/tex] is the output function.. but i still don't get it :(