MHB Convert an automaton into a regular expression

mathmari
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Hey! :o

How can we find the regular expression of a language given by an automaton M??

Could you give some hints?? (Wondering)

Which are the steps that we have to follow so that we convert an automaton into a regular expression?? (Wondering)
 
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This is described in the three books on the theory of computation I recommended.
 
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The following is more or less taken from page 6 of C. Smorynski's "Self-Reference and Modal Logic". (Springer, 1985) (I couldn't get raised brackets to indicate codification (Gödel numbering), so I use a box. The overline is assigning a name. The detail I would like clarification on is in the second step in the last line, where we have an m-overlined, and we substitute the expression for m. Are we saying that the name of a coded term is the same as the coded term? Thanks in advance.

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