MHB What is the General Form of the Language Recognized by the Given Automaton?

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The discussion focuses on determining the general form of the language recognized by a specified automaton with states A (initial), B, C, and D (final). The transition function is provided, and examples of recognized words include 0, 11, and 010*. The user attempts to derive the language using a Generalized Nondeterministic Finite Automaton (GNFA) approach, sequentially removing states and simplifying the expression. The user seeks validation on whether the final expression derived after removing all states accurately represents the language recognized by the automaton. The thread emphasizes the importance of following the correct procedure to ensure the derived language is correct.
evinda
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Hello! (Wave)

I want to write the language of the automaton with the following transition function in regular form with $A$ as an initial state and $B,D$ as final states.

$$\delta:\begin{matrix}
& & 0 & 1\\
& A & B & C\\
& B & C & D\\
& C & D & B\\
& D & D & C
\end{matrix}$$

I have drawn the following dfa:

View attachment 5848

Some of the words that the automaton recognizes are the following:

$$0,11,10,000,01,010^{\star},0000^{\star}, 111, 101110$$

How can we find the general form of the words of the language? (Thinking)
 

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You can use the procedure from the proof of Lemma 1.60 (p. 69) in Sipser's book.
 

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