perfect induction, Theory of Computation

A.(A+C)=A
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Lemma 1 A string w ∈ Σ* is accepted by an LTk automaton iff w is the concatenation of the symbols labeling the edges of a path through the LTk transition graph of A from h?, ∅i to

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what exactly is this and how is it implemented and how to prove its correctness, completeness...

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