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The dragon book lists properties of an NFA N(r) created using Thompson's construction, in particular:

  1. Each state of N(r) other than the accepting state has either one outgoing transition on a symbol in Σ or two outgoing transitions, both on ϵ.

However, the same book shows NFAs created using Thompson's construction that seem to contradict that very statement, like this one:

Figure 3.44: NFA for r3

Here, nodes 3 and 5, which are not accepting states, have only one outgoing ϵ transition each. What am I missing?

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    $\begingroup$ Yes, I think they made a small mistake here, as the rules both for converting $\epsilon$ and a union of two expressions explicitly state that they include states with one $\epsilon$-transition to the accepting state. They probably should have said "Each state ... has either one outgoing transition in $\Sigma\cup\{\epsilon\}$ ...". $\endgroup$
    – Highheath
    Jun 22, 2023 at 12:28

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Thanks @Highheath in the comments, you are right.

At first I found it hard to believe that I should be the first one to have found such an error in the 36+ years since this - apparently very popular - book is out. It is in its second edition since 2008, but I would have expected this part to have been in the first edition as well.

Be that as it may, the error shows up in the errata:

Errata

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