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Refer to the paper Radu Grosu, "Finite Automata as Time Invariant Linear Systems - Observability, Reachability and More". I have a problem understanding the state transition diagram of DMA $M_1$ in Figure 2. It seems that the transition map is only partially defined. In particular, what is the next state by applying $b$ while in state $x_2$ or what is the next state by applying $a$ while in state $x_3$?

Thanks.

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Often that means that there is a transition to a "dead" state which is omitted from the diagram. A "dead" state is a nonaccepting state from which all transitions lead back to the dead state. Does that make sense in the context? –  MJD Mar 22 '12 at 22:17
    
I think it does make sense. Thanks. –  Manos Mar 22 '12 at 22:21
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