Proving Arden's Theorem: A Step-by-Step Explanation 📖

Here we prove Arden's Theorem/Lemma, which says that if we have regexes A and B such that (1) epsilon is not in A, and (2) A = C U AB for some regex C, then we can uniquely write A as CB*. The idea is to "expand" out the right side until we notice a pattern, and then factor C out of the right side. Then we use the definition of star to deduce that it is indeed CB*.

#easytheory #nfa #dfa #gate #gateconcept #theoryofcomputing #turingmachine #nfatoregex #cfg #pda #undecidable #ricestheorem

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▶ADDITIONAL QUESTIONS◀
1. Prove that A = CB* is unique.

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▶ABOUT ME◀
I am a professor of Computer Science, and am passionate about CS theory. I have taught many courses at several different universities, including several sections of undergraduate and graduate theory-level classes.