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According to Schaum's Outlines, the state diagrams of Finite State Machines are labelled directed graphs. Now, it is entirely possible that the resultant state after transition returns to itself more than once for different inputs, but then you'd have to create multiple self loops in the diagram. There are state tables in C.L Liu for the same proposition but without illustrations, so I'm a bit hesitant to draw multiple loops as 1. I haven't seen them so far anywhere, and 2. I haven't come across multiple self loops in graph theory either. Can anyone clarify and if possible, give references?

Bernard
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Shubham Agrawal
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  • Do you mean if it's possible to have multiple self-loops? That's fine, this dfa ( https://stackoverflow.com/questions/10304686/two-inputs-on-self-loop-deterministic-or-non-deterministic-state-machine ) would be a simple example of that – AnilCh May 22 '21 at 12:33
  • You either have to deal with multiple (namely, possibly alphabet-size many) edges between two vertices anyway - then why be afraid of multiple self loops? Or you label edges with multiple inputs (thereby replacing multiple edges with single - multi-labeled - edges) and then can also get away with single but multi-labeled self loops. – Hagen von Eitzen May 22 '21 at 12:33

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